Let f(x)= Cube root(x + 2) and g(x) = x^3 - 2. Which of the following are true?

Question

I. g(x) = f^-1(x) for all the real values of x.
II. (f£»g) (x) = 1 for all reak values of x.
III. The Function is one-to-one.

Answer 1

Lets try the inverse of f(x)

x=cubrt(y+2)
x^3=(y+2
y= x^3-2 so g(x)=inverse of f(x)

lets try f(g(x))=cubrt(x^3-2+2)=x

Now, is it one to one? I will leave that to you to examine.