Assertion :Function satisfying $f (x) = f (2 a - x) \forall x \in R$ is symmetric about the line $x = a$ Reason: Shifting the given function by $a$ units towards negative $x -$ axis makes the function even & even functions are symmetric about $y$ -axis.

Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

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Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

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Assertion is correct but Reason is incorrect

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Both Assertion and Reason are incorrect

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Solution

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
Given $f (x) = f (2 a - x)$
replacing $x \to a + x o r a - x$
$∴ f (a + x) = f (2 a - x - a)$
$\Rightarrow f (a + x) = f (a - x)$
Substituting $x$ with $- x$ proves that function is even
Therefore both Assertion and Reason are correct and Reason is correct explanation

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