Question

Please help!!

Answer 1

Since g(h(x))=h(g(x))= x, hence functions h and g are inverses of each other

Given the functions expressed as:

$h(x) =\sqrt{2x+2}\\g(x)\frac{x^2-2}{2}$

In order to check whether they are inverses of each other, we need to show that h(g(x)) = g(h(x))

Get the composite function h(g(x))

$h(g(x))=h(\frac{x^2-2}{2} )\\h(g(x))=\sqrt{2(\frac{x^2-2}{2} )+2}\\h(g(x))=\sqrt{x^2-2+2} \\h(g(x))=\sqrt{x^2}\\h(g(x))=x$

Get the composite function g(h(x))

$g(h(x))=\frac{(\sqrt{2x+2} )^2-2}{2} \\g(h(x))=\frac{2x+2-2}{2}\\g(h(x))=\frac{2x}{2}\\g(h(x))=x$

Since g(h(x))=h(g(x))= x, hence functions h and g are inverses of each other

Learn more on inverse functions here; brainly.com/question/14391067

Answer 2

Answer:

it’s A

Step-by-step explanation: just took the test