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Statement I : The function is a $f (x) = x^{2} + \tan^{- 1} x$ is a non-periodic function
Statement II: The sum of two non-periodic functions is always non-periodic

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Statement I is true, statement 2 is true, Statement 2 is not correct explanation for statement 1

Statement I is true, statement 2 is true, Statement 2 is correct explanation for statement 1

Statement 1 is true, but statement 2 is false

Statement 1 is false, but statement 2 is true

answer is D.

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Detailed Solution

$f (x) = x^{2} + \tan^{- 1} x$ is non periodic, but sum of wo non periodic functions is not always non periodic as $f (x) = x$ and $g (x) = - [x]$

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