SATHEE: Functions 2 Question 17

Functions 2 Question 17

18.

If $f (x) = {(a - x^{n})}^{1 / n}$ , where $a > 0$ and $n$ is a positive integer, then $f [f (x)] = x$ .

(1983, 1M)

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Answer:

Correct Answer: 18. (True)

Solution:

Given,

$f (x) = {(a - x^{n})}^{1 / n}$

$\Rightarrow f [f (x)] = {[a - {(a - x^{n})}^{1 / n}^{n}]}^{1 / n} = {(x^{n})}^{1 / n} = x$

$∴ f [f (x)] = x$

Hence, given statement is true.

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Functions 2 Question 17

18.

Answer:

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