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Question

# Assertion :A function f satisfies the condition f(x+T)=1+{1âˆ’3f(x)+3(f(x))2âˆ’(f(x))3}1/3(where T is a fixed positive number) is periodic with period 2T. Reason: If f(x+2T)=f(x) then period of f(x) is 2T.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
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 AssertionGiven f(x+T)=1+{1−3f(x)+3(f(x))2−(f(x))3}1/3=1+{(1−f(x))3}13f(x+T)=−f(x)+2⇒f(x+T)+f(x)=2 ....(i)Substituting x→x+T∴f(x+2T)+f(x+T)=2 ......(ii)∴ Subtracting (i) and (ii), we getf(x+2T)−f(x)=0⇒f(x+2T)=f(x)⇒ Period of f(x) is 2TAssertion (A) & Reason (R) both are true & Reason (R) is correct explanation of Assertion (A).

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