TS EAMCET · Maths · Functions
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
- A \(x\)
- B \(x^n\)
- C \(p^{1 / n}\)
- D \(p-x^n\)
Answer & Solution
Correct Answer
(A) \(x\)
Step-by-step Solution
Detailed explanation
Given, \(\quad f(x)=\left(p-x^n\right)^{1 / n}, p>0\) Now, \[ \begin{aligned} f[f(x)] & =f\left[\left(p-x^n\right)^{1 / n}\right] \\ & =\left\{p-\left(p-x^n\right)^{1 / n \times n}\right\}^{1 / n} \\ & =\left(x^n\right)^{1 / n}=x \end{aligned} \]
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