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

Evaluate f(-x): Consider the function f(x)=-x^(3)+x^(5). To determine if the function is even, odd, or neither, we need to evaluate f(-x) and compare it to f(x). Substitute -x for x in f(x)=-x^(3)+x^(5). f(-x)=-(-x)^(3)+(-x)^(5)Simplify function: Simplify the right side of the function. f(-x)=-(-x^3)+(-x^5) f(-x)=-(-x*x*x)+(-x*x*x*x*x) f(-x)=-(x^3)+(-x^5) f(-x)=x^3-x^5Compare f(-x) with f(x): Compare f(-x) with f(x). We have f(x)=-x^3+x^5 and f(-x)=x^3-x^5. Since f(-x) = -f(x), f(x) is an odd function.

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

Determine whether the function $f(x)=-x^{3}+x^{5}$ is even, odd or neither. $\newline$ even $\newline$ odd $\newline$ neither

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Algebra 2

Even and odd functions

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Q. Determine whether the function

f(x)=-x^{3}+x^{5}

is even, odd or neither.

\newline

even

\newline

odd

\newline

neither

Evaluate $f(-x)$ : Consider the function $f(x)=-x^{3}+x^{5}$ . To determine if the function is even, odd, or neither, we need to evaluate $f(-x)$ and compare it to $f(x)$ . Substitute $-x$ for $x$ in $f(x)=-x^{3}+x^{5}$ . $f(-x)=-(-x)^{3}+(-x)^{5}$
Simplify function: Simplify the right side of the function. $\newline$ $f(-x)=-(-x^3)+(-x^5)$ $\newline$ $f(-x)=-(-x\times x\times x)+(-x\times x\times x\times x\times x)$ $\newline$ $f(-x)=-(x^3)+(-x^5)$ $\newline$ $f(-x)=x^3-x^5$
Compare $f(-x)$ with $f(x)$ : Compare $f(-x)$ with $f(x)$ . We have $f(x)=-x^3+x^5$ and $f(-x)=x^3-x^5$ . Since $f(-x) = -f(x)$ , $f(x)$ is an odd function.