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Q.
If $f(x)=\left(100^5-x^{10}\right)^{\frac{1}{10}}$, then the value of $\frac{1}{512} f(f(1024))$ is
Relations and Functions - Part 2
Solution:
$f(f(x))=f\left(100^5-x^{10}\right)^{\frac{1}{10}}=\left(100^5-\left(\left(100^5-x^{10}\right)^{\frac{1}{10}}\right)^{10}\right)^{\frac{1}{10}}=x$
$\Rightarrow f ( f (1024))=1024$
$\frac{1}{512}f(f(1024))=2$