Question

F(x) = 1

2
x and f -1(x) = 2x to solve the problems.

f(2) =

f−1(1) =

f−1(f(2)) =

Answer 1

`f(2) = 1`

`{f}^( - 1) (1) = 2`

`{f}^( - 1) (f(2)) = 2`

Explanation:

The given function is

`f(x ) = (1)/(2)x`

and the inverse function is

`{f}^( - 1) (x) = 2x`

To find f(2), we substitute x=2 into the function f(x)=½x

This implies that,

`f(2) = (1)/(2) (2) = 1`

Similarly,

`{f}^( - 1) (1) = 2(1) = 2`

Based on the above results,

`{f}^( - 1) (f(2)) = {f}^( - 1) (1) = 2`