Question

How do you verify that a function f & g are inverses of each other by showing that f(g(x))=x.
f(x)=3sqrt(x+3)
g(x)=(x-3)^3

Answer 1

If you plug in x=g(x) into f(x) and find that it equals x, and then plug in x=f(x) into g(x) and get x, then the functions are inverses of each other

Answer 2

I.E. f(g(x)) = f( (x-3)^3 )
= 3sqrt( (x - 3)^3 + 3 )

g(f(x)) = g( 3sqrt(x + 3)
= (3sqrt(x + 3) - 3)^3