Question

8. A student claims that f(x) = 4x is the inverse of h(x) = -4x. Is the student correct? Justify your

answer.

Answer 1

The student is not correct.

Explanation:

A function h(x) is the inverse of f(x) if and only if:

`h(f(x))=f(h(x))=x`

We have that f(x)=4x.

And h(x)=-4x.

Let’s verify whether or not they are inverses using the above property.

So:

`h(f(x))=h(4x)`

Therefore:

`h(4x)=-4(4x)=-16x\\eq x`

Likewise:

`f(h(x))=f(-4x)`

Then:

`=4(-4x)=-16x\\eq x`

Since both of the compositions do not result in x, the two functions are not inverses.