Question

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

• A. $f{x}^{\frac{1}{3}}$
• B. $x^3$
• C. $(3-x^3)$
• D. $x$

Answer 1

The correct option is D $x$

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

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

$\Rightarrow fof\left(x\right)={\left(3\right(3-x^3{)}^{\frac{1}{3}\times 3})}^{\frac{1}{3}}$

$\Rightarrow fof\left(x\right)={\left(3\right(3-x^3{)}^1)}^{\frac{1}{3}}$

$\Rightarrow fof\left(x\right)=(3-3+x^3{)}^{\frac{1}{3}}$

$\Rightarrow fof\left(x\right)=(x^3{)}^{\frac{1}{3}}$

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

Hence, $fof\left(x\right)=x$
So, $C$ is the correct answer.