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If $\mathrm{f}$ is an even function and $\mathrm{g}$ is an odd function, then the function fog is
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Verified Answer
The correct answer is:
an even function
We have, $f o g(-x)=f[g(-x)]=f[-g(x)]$ $(\because g$ is odd $)$
$\begin{array}{l}
=\mathrm{f}[\mathrm{g}(\mathrm{x})] \quad(\because \mathrm{fis} \text { even }) \\
=\operatorname{fog}(\mathrm{x}) \forall \mathrm{x} \in \mathrm{R}
\end{array}$
$\therefore$ fog is an even function.
$\begin{array}{l}
=\mathrm{f}[\mathrm{g}(\mathrm{x})] \quad(\because \mathrm{fis} \text { even }) \\
=\operatorname{fog}(\mathrm{x}) \forall \mathrm{x} \in \mathrm{R}
\end{array}$
$\therefore$ fog is an even function.
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