Question

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

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

Answer 1

Answer: (C)

$x$

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

Then,

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

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

$={(3-\{(3-x^3{)}^{1/3}{\}}^3)}^{\frac{1}{3}}$

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

$=(x^3{)}^{\frac{1}{3}}$

$=x$.