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Pepsi [2]
4 years ago
12

How do i solve this question?

Mathematics
1 answer:
Andrews [41]4 years ago
3 0

when it comes to checking if a function is even or odd, it boils down to changing the argument, namely x = -x, and if the <u>resulting function is the same as the original</u>, then is even, if the <u>resulting function is the same as the original but negative</u>, is odd, if neither, well then neither :).


anyway, that said, let's first expand it and then plug in -x,


\bf f(x)=(x^2-8)^2\implies f(x)=(x^2-8)(x^2-8)\implies f(x)=\stackrel{FOIL}{x^4-16x^2+64}\\\\[-0.35em]~\dotfill\\\\f(-x)=(-x)^4-16(-x)^2+64\qquad \begin{cases}(-x)(-x)(-x)(-x)=x^4\\(-x)(-x)=x^2\end{cases}\\\\\\f(-x)=x^4-16x^2+64\impliedby \stackrel{\textit{same as the original}}{Even}

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