What is the inverse function?

1 Answer
Sep 25, 2015

Answer:

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#