Question

If f : R → R be defined by f(x) = (3 − x³)1/3, then find fof (x).

Answer 1

$$\begin{gathered} \left(fof\right)\left(x\right)=f\left(f\left(x\right)\right) \\ =f\left({\left(3-x^3\right)}^{\frac{1}{3}}\right) \\ ={\left[3-{\left({\left(3-x^3\right)}^{\frac{1}{3}}\right)}^3\right]}^{\frac{1}{3}} \\ ={\left[3-\left(3-x^3\right)\right]}^{\frac{1}{3}} \\ ={\left(x^3\right)}^{\frac{1}{3}} \\ =x \end{gathered}$$