Question

Determine whether the functions are inverses1. f(×) = 2(×-4)2. f(×)=(×-1)square + 2

Answer 1

Given the two functions below

`\begin{gathered} f(x)=2(x-4) \\ f(x)=(x-1)^2+2 \end{gathered}`

In other to determine whether the functions are inverse, we would find the inverse of both functions as shown below

`\begin{gathered} f(x)=2(x-4) \\ (f(x))/(2)=x-4 \\ (f(x))/(2)+4=x \\ \text{replace f(x) with x},\text{ and x with f'(x)} \\ \\ (x)/(2)+4=f^(\prime)(x) \\ f^(\prime)(x)=(x)/(2)+4 \end{gathered}`
`\begin{gathered} f(x)=(x-1)^2+2 \\ f(x)-2=(x-1)^2 \\ \sqrt[]{f(x)-2}=x-1 \\ \sqrt[]{f(x)-2}+1=x \\ \text{replace f(x) with x},\text{ and x with f'(x)} \\ \sqrt[]{x-2}+1=f^(\prime)(x) \\ f^(\prime)(x)=\sqrt[]{x-2}+1 \end{gathered}`

It can be observed from the inverse function that none of the inverse functions is equal to the original function of the given question

Hence, the functions are not inverses