Question

If $f:R\to R$ be defined by $f\left(x\right)=(3-x^5{)}^{\frac{1}{5}}$, be defined by $fof\left(x\right)$ is equal to

• A. $x^{\frac{1}{5}}$
• B. $x^3$
• C. $x$
• D. $3-x^5$

Answer 1

The correct option is C $x$

Given $f:R\to R$ be defined by $f\left(x\right)=(3-x^5{)}^{\frac{1}{5}}$.

Now,

$fof\left(x\right)$

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

$=(3-f(x{)}^5{)}^{\frac{1}{5}}$

$={(3-{\left[\right\{3-x^5{\}}^{\frac{1}{5}}]}^5)}^{\frac{1}{5}}$

$=(x^5{)}^{\frac{1}{5}}$

$=x$.