First slide

Extreme values and Periodicity of Trigonometric functions

Question

If $g$ is periodic. Then

Moderate

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 $g o f$

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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