Question

question 7
for the following exercise, determine whether the function is odd, even, or neither.
f(x)=5x - x^3
odd even neither
question help: video message instructor

Explanation:

Step1: Recall the definitions

An even function satisfies $f(-x)=f(x)$ and an odd function satisfies $f(-x)=-f(x)$. First, find $f(-x)$ for $f(x) = 5x - x^{3}$.

Step2: Calculate $f(-x)$

Substitute $-x$ into $f(x)$:
\[

$$\begin{align*} f(-x)&=5(-x)-(-x)^{3}\\ &=- 5x-(-x^{3})\\ &=-5x + x^{3}\\ &=-(5x - x^{3}) \end{align*}$$

\]

Step3: Compare with $f(x)$

Since $f(-x)=-(5x - x^{3})=-f(x)$, the function is odd.

Answer:

odd