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Determine whether the function
f(x)=-8x^(3)-7x^(4) is even, odd or neither.
neither
even
odd

Determine whether the function $f(x)=-8 x^{3}-7 x^{4}$ is even, odd or neither. $\newline$ neither $\newline$ even $\newline$ odd

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Even and odd functions

Full solution

Q. Determine whether the function

f(x)=-8 x^{3}-7 x^{4}

is even, odd or neither.

\newline

neither

\newline

even

\newline

odd

Define function $f(x)$ : Define the function $f(x)$ . The given function is $f(x) = -8x^{3} - 7x^{4}$ . To determine if the function is even, odd, or neither, we need to evaluate $f(-x)$ and compare it to $f(x)$ .
Calculate $f(-x)$ : Calculate $f(-x)$ . $\newline$ Substitute $-x$ for $x$ in $f(x)$ to get $f(-x)$ . $\newline$ $f(-x)=-8(-x)^{3}-7(-x)^{4}$ $\newline$ Now simplify the expression. $\newline$ $f(-x)=-8(-x^3)-7(x^4)$ $\newline$ $f(-x)=8x^3-7x^4$
Compare $f(x)$ and $f(-x)$ : Compare $f(x)$ and $f(-x)$ . We have the original function $f(x) = -8x^{3} - 7x^{4}$ and the transformed function $f(-x) = 8x^{3} - 7x^{4}$ . Now we compare $f(x)$ with $f(-x)$ . Since $f(-x)$ is not equal to $f(x)$ and also not equal to $f(-x)$ $0$ , the function is neither even nor odd.

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