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

answer.

1 Answer

6 votes

Answer:

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.

User Christopher Jones
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