Question

consider the functions f(x)=x^3-2 and g(x)=3 sqrt x+2:
a. find f(g(x))
b. find g(f(x))
c. determine whether the functions f and g are inverse of each other.
I have no clue where to even begin!

Answer 1

f(g) = g^3-2 = (3sqrt(x+2))^3-2 = 27(x+2)sqrt(x+2)-2
g(f) = 3sqrt(f+2) = 3sqrt(x^3) = 3xsqrt(x)

if they are inverses, g(f) = f(g) = x
Obviously they are not inverses

Answer 2

thanks alot