Question

If $f\left(x\right)={(25-x^4)}^{1/4},0<x<\sqrt{5}$, then $f\left(f\left(\frac{1}{3}\right)\right)=$

• A. $\frac{1}{3}$
• B. $3^{1/3}$
• C. $27$
• D. $\frac{2}{3}$

Answer 1

The correct option is A $\frac{1}{3}$

$f\left(f\right(x\left)\right)={(25-(f\left(x\right){)}^4)}^{\frac{1}{4}}\Rightarrow f\left(f\right(x\left)\right)={[25-25+x^4]}^{\frac{1}{4}}\Rightarrow f\left(f\right(x\left)\right)=x\Rightarrow f\left(f\left(\frac{1}{3}\right)\right)=\frac{1}{3}$