Answer:
The student is not correct.
Step-by-step explanation:
A function h(x) is the inverse of f(x) if and only if:
[tex]h(f(x))=f(h(x))=x[/tex]
We have that f(x)=4x.
And h(x)=-4x.
Let’s verify whether or not they are inverses using the above property.
So:
[tex]h(f(x))=h(4x)[/tex]
Therefore:
[tex]h(4x)=-4(4x)=-16x\neq x[/tex]
Likewise:
[tex]f(h(x))=f(-4x)[/tex]
Then:
[tex]=4(-4x)=-16x\neq x[/tex]
Since both of the compositions do not result in x, the two functions are not inverses.
