Question

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

Answer 1

Answer:

$\sqrt{-(x +72)^3} - 72 = -(3\sqrt x - 72 +72)^3$

Step-by-step 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)

$g(h(x)) = 3\sqrt{h(x)} - 72$

Substitute value for h(x)

$g(h(x)) = 3\sqrt{-(x +72)^3} - 72$

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:

$\sqrt{-(x +72)^3} - 72 = -(3\sqrt x - 72 +72)^3$