A table of values for a one-to-one function is given. Find the indicated value.

Question

A table of values for a one-to-one function is given. Find the indicated value.

x	1	2	3	4	5	6
f(x)	6	5	2	0	1	3

f ⁻¹(f(5)) =

**Please walk me through the steps.

Answer 1

The innermost operation is f(5). At x = 5, f(x = 5) = 1, as given. So then you have f^-1(1) when you replace f(5) with 1. The notation f^-1(y) essentially asks for the x at which f(x) = y. For some functions this can be problematic (e.g. periodic functions). The problem states that the function is one-to-one, so when you do f^-1(1) the only point available is 5.