If f(x) is a periodic function with period T, | vedclass

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Question

(D) function $f(x)$ is periodic with period $T$ if $f(x + T) = f(x)$ for all $x$. Let $g(x) = f(ax + b)$. We want to find the period $T'$ such that $g

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$T/a$

Vedclass · Answer

(D) function $f(x)$ is periodic with period $T$ if $f(x + T) = f(x)$ for all $x$. Let $g(x) = f(ax + b)$. We want to find the period $T'$ such that $g(x + T') = g(x)$. $g(x + T') = f(a(x + T') + b) = f(ax + aT' + b)$. For this to be equal to $f(ax + b)$,we must have $aT' = T$. Therefore,$T' = T/a$. Thus,the function $f(ax + b)$ is periodic with period $T/a$.

If $f(x)$ is a periodic function with period $T$,then the function $f(ax + b)$ where $a > 0$,is periodic with period:

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