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Q.

If $g$ is periodic. Then

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a

$f o g$ will always be periodic.

b

$f o g$ need not be periodic

c

$g o f$ will always be periodic

d

The period of g is is same as $g o f$

answer is A.

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Detailed Solution

Since g is periodic $g (x + T) = g (x)$

now $f o g (x + T) = f [g (x + T)]$

$= f (g (x))$

$= f o g (x)$

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