Question

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

f(2)=
f^-1(1) =
f^-1(F(2)) =

Answer 1

Given:

The functions are:

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

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

To find:

The values of
`f(2),f^(-1)(1),f^(-1)(f(2))`.

Solution:

We have,

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

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

Putting
`x=2` in (i), we get

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

`f(2)=1`

Therefore, the value of
`f(2)` is 1.

Putting
`x=1` in (ii), we get

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

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

Therefore, the value of
`f^(-1)(1)` is 2.

Now,

`f^(-1)(f(2))=f^(-1)(1)`
`[\because f(2)=1]`

`f^(-1)(f(2))=2`
`[\because f^(-1)(1)=2]`

Therefore, the value of
`f^(-1)(f(2))` is 2.