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

Question

If f is an even function and g is an odd function, then the function f o g is (A) an even function (B) an odd function (C) neither even nor odd (D) a periodic function

Tardigrade Admin · Accepted Answer

We have, f o g(- x ) = f [ g (- x )] = f [- g ( x )](∵ g is odd ) = f [ g ( x )] (∵ f is even ) = fog ( x ) ∀ x ∈ R ∴ fog is an even function

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

an even function

an odd function

neither even nor odd

a periodic function

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

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