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)=(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*(-2)=-4,\\\\\\f(-4)=(1)/(2)*(-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.`