Question

If $f:R\to R$ be given by $f\left(x\right)=(3-x^3{)}^{\frac{1}{3}}$, then fof (x)is
$\left(a\right)x^{\frac{1}{3}}\left(b\right)x^3$
$\left(c\right)x$
$\left(d\right)3-x^3$

Answer 1

Here, function $f:R\to R$ is given as $f\left(x\right)=(3-x^3{)}^{\frac{1}{3}}$
$\therefore fof\left(x\right)=f\left(f\right(x\left)\right)=f\left(\right(3-x^3{)}^{\frac{1}{3}})=[3-\left(\right(3-x^3{)}^{\frac{1}{3}}{)}^3{]}^{\frac{1}{3}}$
$=[3-(3-x^3){]}^{\frac{1}{3}}=(x^3{)}^{\frac{1}{3}}=x$
$\therefore fof\left(x\right)=x.$ Thus, the correct answer is option (c).