Question

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

F^-1(f(x))= f(f^-1(x))

Answer 1

Answer: the answer is actually X

Explanation:

Answer 2

see the procedure

Explanation:

we have

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

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

step 1

Find
`f^(-1)(f(x))`

substitute the variable x for the function f(x)

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

simplify

`f^(-1)(f(x))=x`

step 2

Find
`f(f^(-1)(x))`

substitute the variable x for the function f^-1(x)

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

simplify

`f(f^(-1)(x))=x`

step 3

Compare

`f^(-1)(f(x))=x`

`f(f^(-1)(x))=x`

therefore

`f^(-1)(f(x))=f(f^(-1)(x))` ---> is verified