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Topic: Inverse function


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In the News (Fri 26 Apr 19)

  
  Inverse Function Definition
The inverse function definition is explored using java applets.
Examine the coordinates of the point (blue) in the graph of f and the coordinates of the point (in red) in the graph of its inverse.
domain of inverse of f = {2,1,5,6} and range of inverse of f = {-4,-3,0,2}.
www.analyzemath.com /Inverse-Function-Definition/Inverse-Function-Definiti.html   (499 words)

  
  NationMaster - Encyclopedia: Inverse (function)
In mathematics, an inverse function is in simple terms a function which "does the reverse" of a given function.
g(x) is the graph of the inverse of f(x).
The graph of g(x) is the graph of the inverse of f(x).
www.nationmaster.com /encyclopedia/Inverse-%28function%29   (569 words)

  
 Reference.com/Encyclopedia/Inverse function
is also used for the (set valued) function associating to an element or a subset of the codomain, the inverse image of this subset (or element, seen as a singleton).
For a function between Euclidean spaces, the inverse function theorem gives a sufficient condition for the function to have a locally defined inverse.
Because the range of a left inverse is not restricted, we can adjoin to the domain of this injection an element "undefined", which we then assign to every element of the codomain which is not in the range.
www.reference.com /browse/wiki/Inverse_function   (835 words)

  
  Kids.Net.Au - Encyclopedia > Inverse function
In mathematical analysis, an inverse function is in simple terms a function which "does the reverse" of a given function.
As such, the prefix arc is sometimes used to denote inverse trigonometric functions[?], eg arcsin x for the inverse of sin x).
For a function f to have a valid inverse, it must be a bijection, that is:
www.kids.net.au /encyclopedia-wiki/in/Inverse_function   (328 words)

  
 Inverse functions - Topics in precalculus
is the inverse function of y = x².
g(x) is the graph of the inverse of f(x).
The graph of g(x) is the graph of the inverse of f(x).
www.themathpage.com /aPreCalc/inverse-functions.htm   (685 words)

  
 PlanetMath: inverse function
The inverse function and the inverse image of a set coincide in the following sense.
For functions between Euclidean spaces, the inverse function theorem gives a necessary and sufficient condition for the inverse to exist.
This is version 7 of inverse function, born on 2003-08-23, modified 2006-08-20.
planetmath.org /encyclopedia/Inverse3.html   (142 words)

  
 [No title]   (Site not responding. Last check: )
To use the inversion method, the inverse function either has to be available explicitly, as in the exponential, Weibull, logistic and Pareto cases, or has to be computable in a reasonable amount of time.
The trigonometrical functions cause difficulties unless the domain for the inverse function is restricted.
Students were asked to identify the kind of functions shown on various graphs - for instance, an inverse function depicted in a graph with two curves back to back in opposite sectors.
www.lycos.com /info/inverse-function.html   (477 words)

  
 1.7 - Inverse Functions
The inverse of the function f is denoted by f
The inverse of a function differs from the function in that all the x-coordinates and y-coordinates have been switched.
If a function passes both the vertical line test (so that it is a function in the first place) and the horizontal line test (so that its inverse is a function), then the function is one-to-one and has an inverse function.
www.richland.edu /james/lecture/m116/functions/inverses.html   (1178 words)

  
 Inverse Functions
To prove that g is the inverse of f we must show that this is true for any value of x in the domain of f.
Note that the reflected graph does not pass the vertical line test, so it is not the graph of a function.
This generalizes as follows: A function f has an inverse if and only if when its graph is reflected about the line y = x, the result is the graph of a function (passes the vertical line test).
www.uncwil.edu /courses/mat111hb/functions/inverse/inverse.html   (1179 words)

  
 BioMath: Functions
Understanding inverse functions will help you solve some of the equations that you will encounter in the life sciences.
For instance, you many have a function that tells you the frequency of an allele in a population at a given point in time.
While we cannot find the inverse of a function that is not one-to-one, often we can find the inverse of such functions by restricting the domain.
www.biology.arizona.edu /BioMath/tutorials/Functions/Inverse.html   (919 words)

  
 Inverse Functions
For functions, there are two conditions for a function to be the inverse function:
The notation used to indicate an inverse function is: f
Notice, that this inverse make sense.  The original problem had adding by two and the inverse is subtracting two.  The original function had multiplying by five and the inverse has division by five.
home.alltel.net /okrebs/page45.html   (381 words)

  
 InverseFunctions.html
Determine whether a given function is one-to-one from its graph.
Functions whose effects can be reversed are said to be invertible.
Note that the graph of the inverse of f (shown in blue) is the reflection of the graph of f (shown in red) across the line y = x (shown in green).
dl.uncw.edu /digilib/mathematics/algebra/functions/freeze/InverseFunctions.html   (574 words)

  
 PlanetMath: inverse function theorem
The inverse function theorem is a special case of the implicit function theorem where the dimension of each variable is the same.
Cross-references: variable, dimension, implicit function theorem, strictly monotonic function, monotonic, strictly, neighbourhood, open interval, function, Jacobian, point, open set, mapping, vector-valued function, continuously differentiable
This is version 6 of inverse function theorem, born on 2002-08-24, modified 2002-12-28.
planetmath.org /encyclopedia/InverseFunctionTheorem.html   (118 words)

  
 Math B - Definition of Inverse Function
For all one-to-one functions, the inverse function is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function.
Since function f was not a one-to-one function (the y value of 1 was used twice), the inverse will NOT be a function (because the x value of 1 now gets mapped to two separate y values which is not possible for functions).
It may be necessary to restrict the domain on certain functions to guarantee that the inverse is also a function.
regentsprep.org /Regents/mathb/7a3/inverselesson.htm   (518 words)

  
 Inverse Activity
I expect students to know that the inverse of 2/3 is 3/2, but I want to make sure they understand that this is because when you multiply 2/3 by its inverse, 3/2, you get 1, the multiplicative identity.
See that the inverse of an unrestricted parabolic function is not a function.
In words, f is the function that subtracts 3 from x and then divides by 2.
www.tcnj.edu /~golazes2/inverse_activity.htm   (614 words)

  
 Math B - Definition of Inverse Function
For all one-to-one functions, the inverse function is the set of ordered pairs obtained by interchanging the first and second elements of each pair in the original function.
Since function f was not a one-to-one function (the y value of 1 was used twice), the inverse will NOT be a function (because the x value of 1 now gets mapped to two separate y values which is not possible for functions).
by restricting the graph in such a manner, you guarantee the existence of an inverse function for a portion of the graph.
www.regentsprep.org /Regents/mathb/7a3/inverselesson.htm   (518 words)

  
 Math Forum - Ask Dr. Math Archives: Inverse of a Function
I would like to know if you have a good example of how inverse functions would be used in real life.
Consider as a function from R -> R (Real) and say whether the function is invertible: h(x) = (sgn x)* sqrt(abs(x)) where sgn is +1 if x is positive, -1 if x is negative, and 0 if x is 0.
Finding the inverse of a function and graphing yields a graph that has been reflected in the line y = x relative to the function.
mathforum.org /library/drmath/sets/select/dm_inverse_func.html   (382 words)

  
 Trigonometric Functions - Inverse Trig. Functions and their Graphs   (Site not responding. Last check: )
A function has an inverse function strictly when no horizontal line intersects the graph more than once.
functions don't have inverse functions, and it is useful to have an inverse function, a restriction is applied to the domain so that an inverse function might exist.
The range of the function with its restricted domain is the same as the range of the original function.
library.thinkquest.org /10030/2inverse.htm   (236 words)

  
 Inverse function - Definition, explanation
In mathematics, an inverse function is in simple terms a function which "does the reverse" of a given function.
As such, the prefix arc is sometimes used to denote inverse trigonometric functions, e.g.
is also used for the (set valued) function associating to an element or a subset of the codomain, the inverse image of this subset (or element, seen as a singleton).
www.calsky.com /lexikon/en/txt/i/in/inverse_function.php   (539 words)

  
 Inverse Functions: Definition / Drawing Inverses
The inverse of a function has all the same points, except that the
You can see on this last picture that there is a definite graphical relationship between the points of the function and the points of the inverse.
don't move; that is, where the function crosses the diagonal, the inverse will cross, too.
www.purplemath.com /modules/invrsfcn.htm   (463 words)

  
 Online Tutorials on Functions and Algebra
Examples on how to aplly and use inverse functions in real life situations and solve problems in mathematics.
Several questions with detailed solutions as well as exercises with answers on how to prove that a given function is a one to one function.
The proof of a formula that gives the inverse of an invertible 2 x 2 matrix is also included.
www.analyzemath.com /PrecalculusTutorials.html   (748 words)

  
 Math Forum Discussions - Re: What is the inverse function of -- y = 2 ^ (x / 18) + (x / 5)
Re: What is the inverse function of -- y = 2 ^ (x / 18) + (x / 5)
> function cannot be written in closed form in terms of "familiar" functions.
The Math Forum is a research and educational enterprise of the Drexel School of Education.
www.mathforum.org /kb/thread.jspa?forumID=56&threadID=182207&messageID=688131   (221 words)

  
 Inverse Function Theorem Exercise
The purpose of this exercise is to use an applet and a graphing calculator to understand what the Inverse Function Theorem says and visualize why it is true.
Find the inverse of this linear function in the usual way, by solving for x in terms of y and then exchanging the variables x and y.
Thus the inverse of the linear function is f
www.mph.net /coelsner/jsp_applets/InvFunThm_ex.htm   (539 words)

  
 Question Corner -- How To Graph The Inverse Of A Function
It is actually easier to graph the inverse of a function than it is to solve for it.
If g is the inverse function of f, then to graph g we'd plot the points (x,y) where y=g(x).
If the function doesn't have an inverse, it is because there are two distinct values a and b which we can assign to x to get the same value for f(x).
www.math.toronto.edu /mathnet/questionCorner/inversegraph.html   (453 words)

  
 Inverse Functions
Restrict the domain of a function that is not one-to-one so that an inverse function can be found
Draw the graph of the inverse function given the graph of the function
Choose a largest possible domain containing the number 100 so that the function restricted to the domain is one-to-one.
www.public.asu.edu /~kamman/notes/inverses/Inverse-Functions.html   (227 words)

  
 Visual Calculus - Inverses of Functions
to recognize from the graph of a function whether the function is one to one;
There is a function g such that gf(x) = x for all x in D and fg(y) = y for all y in R.
If the function f is increasing or decreasing then f has an inverse g.
archives.math.utk.edu /visual.calculus/0/inverse.6/index.html   (253 words)

  
 Inverse function theorem - Definition, explanation
In mathematics, the inverse function theorem gives sufficient conditions for a vector-valued function to be invertible on an open region containing a point in its domain.
That is, an inverse function to f exists in some neighborhood of f(p).
The inverse function theorem can be generalized to differentiable maps between differentiable manifolds.
www.calsky.com /lexikon/en/txt/i/in/inverse_function_theorem.php   (241 words)

  
 Inverse Trigonometric Functions
You probably remember from high school that there are many occassions in which an angle is specified by giving the value of one of the trigonometric functions at this angle.
In that case, you use an inverse function---namely, the square root function---which undoes the operation of the squaring function.
In the same way, we will want to build an inverse tangent function which undoes the operation of the tangent function.
www.ugrad.math.ubc.ca /coursedoc/math100/notes/zoo/invtrig.html   (297 words)

  
 Index to how to solve, compose, translate, find inverse of functions,domain, range.
Index to how to solve, compose, translate, find inverse of functions,domain, range.
Given a function and its value, determine x: Quadratic:
Given a function and its value, determine x: Cubic:
www.jtaylor1142001.net /calcjat/Contents/CFunctions.html   (72 words)

  
 Inverse Function Theorem - Explanation   (Site not responding. Last check: )
The inverse function theorem tells us that, under certain conditions, a differentiable function is invertible near a point a if its derivative at a is invertible.
The derivative of f is a linear map from n-space to n-space.
Return to the main document on the implicit function theorem.
www.ualberta.ca /dept/math/gauss/fcm/calculus/multvrbl/basic/ImplctFnctns/invrs_fnctn_explntn.htm   (166 words)

  
 inverse function: definition, usage and pronunciation - YourDictionary.com   (Site not responding. Last check: )
inverse function: definition, usage and pronunciation - YourDictionary.com
A function whose relation to a given function is such that their composite is the identity function.
It is often found by interchanging dependent and independent variables.
www.yourdictionary.com /ahd/i/i0214650.html   (35 words)

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