What is the inverse function?

1 Answer
Sep 25, 2015

If f is a function, then the inverse function, written f^(-1), is a function such that f^(-1)(f(x)) = x for all x.

Explanation:

For example, consider the function:

f(x) = 2/(3-x)

(which is defined for all x != 3)

If we let y = f(x) = 2/(3-x), then we can express x in terms of y as:

x = 3-2/y

This gives us a definition of f^-1 as follows:

f^(-1)(y) = 3-2/y

(which is defined for all y != 0)

Then f^(-1)(f(x)) = 3-2/f(x) = 3-2/(2/(3-x)) = 3-(3-x) = x