Question

Use f(x) = 1)2 and f^-1(x) = 2x to solve the problems. a) f(2) b)f^-1(1) c)f^-1(f(2))​

Answer 1

a) f (2)  = 1

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

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

Step-by-step explanation:

$f^{-1}$ - Indicates that we have to find the inverse of the function

Given data:

$f(x)=\left(\frac{1}{2}\right) x$ --------> eq.1

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

To find $f(2), f^{-1}(1), f^{-1}(f(2))$

Case a)

Now, substitute x = 2 in the equation 1 to find f (2)

 $f(2)=\left(\frac{1}{2}\right) \times 2=1$

Case b)

Now, substitute x = 1 in the equation 2 to find  $f^{-1}(1)$

  $f^{-1}(1)=2(1)=2$

Case c)

In general,

    $f^{-1}(f(x))=f\left(f^{-1}(x)\right)=x$

Thereby,

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