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JEE MATHEMATICS MCQ: FUNCTIONS

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Let f:R→Rf: R \rightarrow R be continuous and periodic with period T>0T > 0. Then
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Correct option: A
f(x0+T/2)=f(x0)f\left(x_0+T / 2\right)=f\left(x_0\right) for some x0∈[k,k+T/2],k∈Rx_0 \in[k, k+T / 2], k \in R
Option A (f(x0+T/2)=f(x0)f\left(x_0+T / 2\right)=f\left(x_0\right) for some x0∈[k,k+T/2],k∈Rx_0 \in[k, k+T / 2], k \in R) is correct because it applies the Intermediate Value Theorem to show the existence of a point where the function's value at x_0 + T/2 equals its value at x_0.

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