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Determine whether the function
f(x)=x^(3)-5x-9x^(5) is even, odd or neither.
neither
even
odd

Determine whether the function $f(x)=x^{3}-5 x-9 x^{5}$ 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)=x^{3}-5 x-9 x^{5}

is even, odd or neither.

\newline

neither

\newline

even

\newline

odd

Select function for $f(-x)$ : $f(x)= x^3-5x-9x^5$ $\newline$ Select the function for $f(-x)$ . $\newline$ Substitute $-x$ for $x$ in $f(x)= x^3-5x-9x^5$ . $\newline$ $f(-x)= (-x)^3-5(-x)-9(-x)^5$
Substitute $-x$ in $f(x)$ : $f(-x)= (-x)^3-5(-x)-9(-x)^5$ $\newline$ Simplify the right side of the function. $\newline$ $f(-x)= -x^3+5x+9x^5$
Simplify $f(-x)$ : We have: $\newline$ $f(x)= x^3-5x-9x^5$ $\newline$ $f(-x)= -x^3+5x+9x^5$ $\newline$ Is the function $f(x)$ even, odd, or neither? $\newline$ We have $f(x)= x^3-5x-9x^5$ and $f(-x)= -x^3+5x+9x^5$ . $\newline$ Since $f(-x) = -f(x)$ , $f(x)$ is an odd function.

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