Inverse
Functions
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In a Nut Shell: You can think of inverse
functions as two functions with one reversing the action of the
other. An analogy is multiplication
and division in algebra. Note: Not all functions have an
inverse. Guidelines for inverse functions If x1 ≠
x2 implies that f(x1) ≠ f(x2) , then f(x) is said to be one-to-one. An example of a one-on-one
function is the following function, f(x) =
y = 1/x
for x > 0 For each value of x, there is only one
value of y(x). a. Also if
f(x) is one-to-one, then it
has an inverse function, f -1(x). b. If
g is the inverse of f, then
f is the inverse of g. c. The domain of f -1 is equal to the range of f
and the range of f -1 is equal to the domain of f. d. A function need not have an inverse, but if
it does, the inverse function is unique. |
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Strategy to find the
inverse function of a one-to-one function, f.
Click here for information
on implicit differentiation. |
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