Question

Use f(x)=1/2x and f^-1(x)=2x to solve the problems f^1(-2), f(-4), f(f^-1(-2)?

Answer 1

f^1(-2) = 2(-2) = -4
f(-4) = 1/2 * -4 =  -2

f(f^-1(x)) = x    so answer is  -2

Answer 2

Answer:  The required values are

$f^{-1}(-2)=-4,~~f(-4)=-2,~~f(f^{-1}(-2))=-2.$

Step-by-step explanation:  We are given a function f(x) and its inverse as follows :

$f(x)=\dfrac{1}{2}x,\\\\\\f^{-1}(x)=2x.$

We are to find the values of $f^{-1}(x),~f(-4),~f(f^{-1}(-2)).$

The values are evaluated in the following manner :

$f^{-1}(-2)=2\times(-2)=-4,\\\\\\f(-4)=\dfrac{1}{2}\times(-4)=-2,\\\\\\f(f^{-1}(-2))=f(-4)=-2.$

Thus, the required values are

$f^{-1}(-2)=-4,~~f(-4)=-2,~~f(f^{-1}(-2))=-2.$