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

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

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Even and odd functions

Full solution

Q. Determine whether the function

f(x)=7 x^{3}+3 x^{4}+4 x

is even, odd or neither.

\newline

neither

\newline

odd

\newline

even

Select function for $f(-x)$ : $f(x)=7x^3+3x^4+4x$ $\newline$ Select the function for $f(-x)$ . $\newline$ Substitute $-x$ for $x$ in $f(x)=7x^3+3x^4+4x$ . $\newline$ $f(-x)=7(-x)^3+3(-x)^4+4(-x)$
Substitute $-x$ in $f(x)$ : $f(-x)=7(-x)^3+3(-x)^4+4(-x)$ Simplify the right side of the function. $f(-x)=7(-x)^3+3(-x)^4-4x$ $f(-x)=-7x^3+3x^4-4x$
Simplify right side: We have: $\newline$ $f(x)=7x^3+3x^4+4x$ $\newline$ $f(-x)=-7x^3+3x^4-4x$ $\newline$ Is the function $f(x)$ even, odd, or neither? $\newline$ We have $f(x)=7x^3+3x^4+4x$ and $f(-x)=-7x^3+3x^4-4x$ . $\newline$ Since $f(-x)$ is not equal to $f(x)$ and $f(-x)$ is not equal to $-f(x)$ , $f(x)$ is neither even nor odd.

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