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

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

is even, odd or neither.

\newline

neither

\newline

even

\newline

odd

Define function $f(x)$ : Define the function $f(x)$ and consider the function for $f(-x)$ . Substitute $-x$ for $x$ in $f(x)=x^5-3$ . $f(-x)=(-x)^5-3$
Substitute $-x$ : Simplify the right side of the function. $\newline$ $f(-x)=(-x)^5-3$ $\newline$ Since the exponent is odd, $(-x)^5$ becomes $-x^5$ . $\newline$ $f(-x)=-x^5-3$
Simplify function: Compare $f(x)$ with $f(-x)$ . We have: $f(x)=x^5-3$ $f(-x)=-x^5-3$ 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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