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

Answer:

k=2

Step-by-step explanation:

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

$f^{-1}(x)=\frac{1}{4}x+k$

We have to find the value of k.

We have f(x)=4x-8

Let y=4x-8

Then , 4x=y+8

$x=\frac{y+8}{4}$

$x=\frac{1}{4}y+2$

Then ,$f^{-1}(x)=\frac{1}{4}x+2$

Comparing with given inverse function then we get '

k=2

Hence, the value of k must be 2.