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  4. If f is an even function and g is an odd function, then the function f o g is

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Q. If $f$ is an even function and $g$ is an odd function, then the function $f o g$ is

Relations and Functions - Part 2

Solution:

We have, $f o g(- x ) = f [ g (- x )] $
$= f [- g ( x )](\because g$ is odd )
$= f [ g ( x )] (\because f $ is even )
$= fog ( x ) \forall x \in R$
$\therefore $ fog is an even function