Class 12 Relations And Functions · Assertion Reason1 Marksfunction_operations

Class 12 Maths · Relations And Functions · Assertion Reason #61

Assertion: If \(f,g:\mathbb{R}\to\mathbb{R}\), \(f\) is even and \(g\) is odd, then their product \(h(x)=f(x)g(x)\) is odd. Reason: For every real \(x\), evenness and oddness give \(f(-x)=f(x)\) and \(g(-x)=-g(x)\).

(A) Both Assertion and Reason are correct, and the Reason is the correct explanation of the Assertion.
(B) Both Assertion and Reason are correct, but the Reason is not the correct explanation of the Assertion.
(C) The Assertion is correct, but the Reason is incorrect.
(D) The Assertion is incorrect, but the Reason is correct.

✅ Step-by-Step Solution

Final Answer: Option (A): Both Assertion and Reason are correct, and the Reason is the correct explanation of the Assertion.

Both statements are true. The Reason directly gives \(h(-x)=f(-x)g(-x)=f(x)(-g(x))=-h(x)\), which proves the Assertion. Therefore a is correct for this explicitly adapted version.

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Class 12 Maths · Relations And Functions · Assertion Reason #61

✅ Step-by-Step Solution

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