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  4. f(x)=( sin x7) ⋅ ex5 operatornamesgn x9 is

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Q. $f(x)=\left(\sin x^{7}\right) \cdot e^{x^{5} \operatorname{sgn} x^{9}}$ is

Trigonometric Functions

Solution:

$f(x)=\left(\sin x^{7}\right) e^{x^{5} \,sgn\, x^{9}}$
$\sin x^{7} \rightarrow$ odd, $\,sgn \,x^{9} \rightarrow$ odd, $x^{5} \rightarrow$ odd
$\therefore e^{x^{5}\, sgn\, x^{9}} \rightarrow$ even
$ \therefore f(x)=$ odd $\times$ even $=$ odd