Question

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

Answer 1

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

Now,

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

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

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

$=(x^3{)}^{1/3}=x$