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

x=9 y=1Step-by-step explanation:...

8. A student claims that f(x) = 4x is the inverse

Kennabug4503

12.02.2022

The student is not correct.

Step-by-step 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:

$h(4x)=-4(4x)=-16x\neq x$

Likewise:

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

Then:

$=4(-4x)=-16x\neq x$

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

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