QuestionDetermine if the function $f(x)=x^{5}-2x^{3}$ is even, odd, or neither algebraically.

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=x^{5}-x^{3}$ . A function $f(x)$ is said to be even if $f(-x) = f(x)$ for all $x$ in the domain of $f$
3. A function $f(x)$ is said to be odd if $f(-x) = -f(x)$ for all $x$ in the domain of $f$
4. If a function is neither even nor odd, then it does not satisfy either of the above conditions

STEP 2

First, we need to find the value of $f(-x)$ .
$f(-x) = (-x)^{5}-2(-x)^{}$

STEP 3

implify the expression.
$f(-x) = -x^{5}+2x^{3}$

STEP 4

Now, compare $f(-x)$ with $f(x)$ and $-f(x)$ .
$f(x) = x^{}-2x^{3}$ $-f(x) = -x^{}+2x^{3}$

STEP 5

From the above comparison, we can see that $f(-x)$ is equal to $-f(x)$ .
Therefore, the function $f(x)=x^{5}-2x^{3}$ is odd.

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