Question

Manish writes the functions g(x)= 3 sqrt -x - 72 and h(x) = -(x + 72)^3

Which pair of expressions could Manish use to show that g(x) and h(x) are inverse functions?

Answer 1

Its c

explanation:

on edge

Answer 2

`√(-(x +72)^3) - 72 = -(3\sqrt x - 72 +72)^3`

Explanation:

Given

`g(x) = 3\sqrt x - 72`

`h(x) = -(x +72)^3`

Required

Show that they are inverse functions

For g(x) and h(x) to be inverse, then:

`g(h(x)) = h(g(x))`

We have:

`g(x) = 3\sqrt x - 72`

Replace x with h(x)

`g(h(x)) = 3√(h(x)) - 72`

Substitute value for h(x)

`g(h(x)) = 3√(-(x +72)^3) - 72`

Similarly;

`h(x) = -(x +72)^3`

Replace x with g(x)

`h(g(x)) = -(g(x) +72)^3`

Substitute value for g(x)

`h(g(x)) = -(3\sqrt x - 72 +72)^3`

Recall that:

`g(h(x)) = h(g(x))`

So:

`√(-(x +72)^3) - 72 = -(3\sqrt x - 72 +72)^3`