 The Inverse of a Function,
a selection of answers from the Dr. Math archives.
 Inverses
 What is an inverse?
 Inverse Statements
 Say there are 3 + 4 times as many girls as boys. Is this the same
as saying there are 3 + 1/4 as many boys as girls?
 Inverting Functions
 To find the inverse of a function y=f(x), do I interchange the
variables x and y, or do I solve for x in terms of y?
 Inverse Functions in Real Life
 I would like to know if you have a good example of how inverse functions
would be used in real life.
 Is the Function Invertible?
 For the following functions f(x) decide if the function is invertible
as a function from R to R...
 Invertible Functions
 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 an Inverse
Function
 What is the inverse function of f(x) = 1  2x? What is the
general method for finding an inverse function?
 Is the Inverse a Function?
 How do I find the inverses and determine whether the inverses are
functions?
 Unraveling an Inverse Function
 I got this question wrong: y = (5x  2) / (x + 1).
 Function Its Own Inverse
 Show that f(x) = X/X1 is its own inverse.
 Inverses of Trigonometric
Functions
 How can the functions cosine and sine have inverses of
arcsin and arccos respectively?
 Inverse Functions: Arcsec(x)
 If y = arcsec(x) then what does x equal? How is this problem
related to inverse functions?
 Inverse of a Function vs.
Inverse Proportionality
 Finding the inverse of a function and graphing yields a graph that has
been reflected in the line y = x relative to the function. Inverse
proportionality, however, yields a reciprocal relation graphically. Why do
these two things have similar names yet mean different things?
 Inverse Functions OneWay Only
 Are there two functions, f and g, such that (f of g)(x) = x but
(g of f)(x) does not equal x?
 Domain and Range of an Inverse Function
 Why is the domain of a function equal to the range of the inverse function?
 Inverse Functions  Which Statement
is True?
 Does (f o g)^(1) equal f^(1) o g^(1) or g^(1) o f^(1)?
How can you prove it?
 Inverse of a Multivariate Function
 Let f:NxN > N such that f(x,y) = 2^x(2y + 1)  1 for all
natural numbers x, y. Let the inverse of f, g be given by g:N > NxN.
Find the inverse of the function g.
