Question

If $f:R\to R$ defined by $f\left(x\right)=(3-x^3{)}^{\frac{1}{3}}$, then find $\left(fof\right)\left(x\right).$

Answer 1

$f:R\to R$

$f\left(x\right)=(3-x^3{)}^{1/3}$

$fof\left(x\right)=f\left(f\right(x\left)\right)$

$=(3-[f\left(x\right){]}^3{)}^{1/3}$

$=[3-(3-x^3{)}^3{]}^{1/3}$

$\Rightarrow [3-(3^3-{3.3}^2.x^3+\mathrm{3.3.}{x}^6-x^9){]}^{1/3}$

$\Rightarrow [3-27+27x^3-9x^6+x^9{]}^{1/3}$

$\Rightarrow [27x^3-9x^6+x^9-24{]}^{1/3}$