Question

consider the functions f(x)=x^3-3 and g(x)=3 sqrt x+3:

a. find f(g(x))
b. find g(f(x))
c. determine whether the functions f and g are inverses of each other.

I really need help with these, I don't get it at all.

Answer 1

I'll do f(g). Then g(f) should be no trouble.

You know f(x) = x^3-3, so
f(g) = g^3-3
But what's g? g(x) = 3√(x+3). So,

f(g) = g^3-3 = (3√(x+3))^3 - 3
= 27(x+3)√(x+3)-3
= 3(9(x+3)^(3/2) - 1)

now, g(f) = 3√(f+3)
...

Answer 2

To be honest, I really don't know how to do any of it:(