If $f(x)=\left(a-x^{n}\right)^{1 / n}$, where $a>0$ and $n$ is a positive integer, then $f[f(x)]=x$.
(1983, 1M)
Correct Answer: 18. (True)
Solution:
$ f(x)=\left(a-x^{n}\right)^{1 / n} $
$\Rightarrow f[f(x)]=\left[a-{\left(a-x^{n}\right)^{1 / n} }^{n}\right]^{1 / n}=\left(x^{n}\right)^{1 / n}=x $
$\therefore f[f(x)]=x$
Hence, given statement is true.
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