If f(x)= (25-x^4 )^ 1 / 4 for 0 < x<5, then f (f (1 2 ) )= - Vidyadip

MCQ

If $f(x)=\left(25-x^4\right)^{1 / 4}$ for $0 < x<\sqrt{5}$, then $f\left(f\left(\frac{1}{2}\right)\right)=$

A
$2^{-4}$
B
$2^{-3}$
C
$2^{-2}$
✓
$2^{-1}$

✓

Answer

Correct option: D.

$2^{-1}$

(D)
Here, $f \left(\frac{1}{2}\right)=\left(25-\frac{1}{16}\right)^{\frac{1}{4}}=\left(\frac{399}{16}\right)^{\frac{1}{4}}$
$\Rightarrow f \left[ f \left(\frac{1}{2}\right)\right]= f \left(\left(\frac{399}{16}\right)^{\frac{1}{4}}\right)$
$=\left(25-\frac{399}{16}\right)^{\frac{1}{4}}$
$=\left(\frac{1}{16}\right)^{\frac{1}{4}}$
$=\frac{1}{2}$

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