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:

$f(x)=\dfrac{1}{2}x$

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

To find:

The values of $f(2),f^{-1}(1),f^{-1}(f(2))$.

Solution:

We have,

$f(x)=\dfrac{1}{2}x$          ...(i)

$f^{-1}(x)=2x$                   ...(ii)

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

$f(2)=\dfrac{1}{2}(2)$

$f(2)=1$

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.