Question

Find \( f \circ g \) and \( g \circ f \) if \[ f(x) = 8x^3 \quad \text{and} \quad g(x) = x^{1/3}. \]

Hint:

To find composition \( f \circ g \), substitute \( g(x) \) into \( f \). For \( g \circ f \), substitute \( f(x) \) into \( g \).

Answer 1

\[ (f \circ g)(x) = f(g(x)) = f\left(x^{1/3}\right) = 8 \left(x^{1/3}\right)^3 = 8x. \] \[ (g \circ f)(x) = g(f(x)) = g(8x^3) = \left(8x^3\right)^{1/3} = 8^{1/3} \cdot (x^3)^{1/3} = 2x. \]