Question

If $f(x)={\left(100^5-x^{10}\right)}^{\frac{1}{10}}$, then the value of $\frac{1}{512}f(f(1024))$ is

• A. 1
• B. 2
• C. 0
• D. 3

Answer 1

Answer: (B)

$f(f(x))=f{\left(100^5-x^{10}\right)}^{\frac{1}{10}}={\left(100^5-{\left({\left(100^5-x^{10}\right)}^{\frac{1}{10}}\right)}^{10}\right)}^{\frac{1}{10}}=x$
$\Rightarrow f(f(1024))=1024$
$\frac{1}{512}f(f(1024))=2$