Question

find the inverse of g(x)=(x+7)^3+4

Answer 1

swap x and g and then solve for g:

x=(g+7)^3+4
x-4 = (g+7)^3
∛(x-4) = g+7
g = ∛(x-4) - 7

check.
If h is g inverse,
g(h(x)) = h(g(x)) = x

g(h) = (h+7)^3+4
= ((∛(x-4) - 7)+7)^3+4
= (∛(x-4)-7+7)^3+4
= ∛(x-4)^3+4
= x-4+4
= x

and similarly for h(g)