Question

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

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

Answer 1

Answer: (C)

x

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

Now,

$fof\left(x\right)$

$=f\left[f\right(x\left)\right]$

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

$={(3-[(3-x^3{)}^{\frac{1}{3}}{]}^3)}^{\frac{1}{3}},$

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

$=[x^3{]}^{\frac{1}{3}}$

$=x$.