If ( 2 )  = f ( 6 ) , then

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Mathematics - Functions Question with Solution | TestHub

MathematicsFunctionsPeriodic FunctionsMedium2 minQB

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Passage / Comprehension

Let $f : R \to R$ be a function satisfying $f (2 - x) = f (2 + x)$ and $f (20 - x) = f (x)$ , $\forall x \in R$ . For this function, answer the following.

If $(2) \neq = f (6)$ , then

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Answer:

Solution:

If 1 is a period, then $f (x) = f (x + 1), \forall x \in R$ $\Rightarrow f (2) = f (3) = f (4) = f (5) = f (6)$ Which contradicts the given hypotheses that $f (2) \neq = f (6)$ $∴ 1 cannot be period of f (x)$

Stream:JEESubject:MathematicsTopic:FunctionsSubtopic:Periodic Functions

⏱ 2mℹ️ Source: QB

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