Question

A student claims that the inverse of f(x)=4x−8f(x)=4x−8 is f−1(x)=14x+k.f−1(x)=14x+k. For the case where the student's claim is true, what must be the value of k?

Answer 1

k=2

Explanation:

We are given that f(x)=4x-8[/tex] and inverse of the given function

`f^(-1)(x)=(1)/(4)x+k`

We have to find the value of k.

We have f(x)=4x-8

Let y=4x-8

Then , 4x=y+8

`x=(y+8)/(4)`

`x=(1)/(4)y+2`

Then ,
`f^(-1)(x)=(1)/(4)x+2`

Comparing with given inverse function then we get '

k=2

Hence, the value of k must be 2.