If $f(x)=\left(p-x^n\right)^{1 / n}, p0$ and $n$ is a positive integer, then $f[f(x)]$ is equal to

Question

If $f(x)=\left(p-x^n\right)^{1 / n}, p>0$ and $n$ is a positive integer, then $f[f(x)]$ is equal to

Aicharya · Accepted Answer

Given, $\quad f(x)=\left(p-x^night)^{1 / n}, p>0$ Now, $ \begin{aligned} f[f(x)] & =f\left[\left(p-x^night)^{1 / n}ight] \ & =\left\{p-\left(p-x^night)^{1 / n 	imes n}ight\}^{1 / n} \ & =\left(x^night)^{1 / n}=x \end{aligned} $

If $f(x)=\left(p-x^n\right)^{1 / n}, p>0$ and $n$ is a positive integer, then $f[f(x)]$ is equal to

Solution