f(x)=(sinx⁷)e^{(x^5 Sgn(x)^9) is
a.odd b.even c.neither d.constant}

Dear Student,
Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{We} \mathrm{have} \\ \mathrm{f}\left(\mathrm{x}\right)=\left({\mathrm{sinx}}^7\right){\mathrm{e}}^{{\mathrm{x}}^5 \mathrm{sgn}\left({\mathrm{x}}^9\right)} \\ \mathrm{f}\left(-\mathrm{x}\right)=\left\{\sin {\left(-\mathrm{x}\right)}^7\right\}{\mathrm{e}}^{{\left(-\mathrm{x}\right)}^5\mathrm{sgn}\left\{{\left(-\mathrm{x}\right)}^9\right\}} \\ =\left\{-{\mathrm{sinx}}^7\right\}{\mathrm{e}}^{{\left(-\mathrm{x}\right)}^5\mathrm{sgn}\left\{{\left(-\mathrm{x}\right)}^9\right\}} \left[\mathrm{As} \sin \left(-\mathrm{A}\right)=-\sin \left(\mathrm{A}\right)\right] \\ =\left\{-{\mathrm{sinx}}^7\right\}{\mathrm{e}}^{-{\mathrm{x}}^5\mathrm{sgn}\left\{-{\mathrm{x}}^9\right\}} \\ =\left\{-{\mathrm{sinx}}^7\right\}{\mathrm{e}}^{+{\mathrm{x}}^5\mathrm{sgn}\left\{{\mathrm{x}}^9\right\} } \left[\mathrm{As} \mathrm{sgn}\left(-\mathrm{A}\right)=-\mathrm{sgn}\left(\mathrm{A}\right)\right] \\ =-\left({\mathrm{sinx}}^7\right){\mathrm{e}}^{{\mathrm{x}}^5 \mathrm{sgn}\left({\mathrm{x}}^9\right)} \\ \mathrm{As} \\ \mathrm{f}\left(-\mathrm{x}\right)=-\mathrm{f}\left(\mathrm{x}\right) \\ \mathrm{Hence} \mathrm{f}\left(\mathrm{x}\right) \mathrm{is} \mathrm{an} \mathrm{odd} \mathrm{function}. \end{gathered}$$

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