Manish writes the functions g of x is equal to cube root of negative x minus 72 and h of x is equal to negative open paren x plus 72 close paren cubed Which pair of expressions could Manish use to show that g of x and h of x are inverse functions?

To check that the functions are inverses, substitute each function into the other. Since h(x)=−(x+72)³, g(h(x))=∛((x+72)³)−72=x. In the other order, h(g(x))=−(∛(−x)−72+72)³=−(∛(−x))³=x. Choice D gives these two expressions, so both compositions simplify to x.

AI-written and checked against the verified answer.