Question

part 2 of 4
(b) find -k(x).
-k(x) = -8x³ - 3x
part 3 of 4
(c) is k(-x) = -k(x)?
k(-x) dropdown -k(x)
part: 3 / 4
part 4 of 4
(d) is this function even, odd, or neither?
the function is select

Explanation:

Step1: Deduce $k(x)$ from $-k(x)$

Given $-k(x) = -8x^3 - 3x$, multiply both sides by $-1$:
$k(x) = 8x^3 + 3x$

Step2: Calculate $k(-x)$

Substitute $x$ with $-x$ in $k(x)$:
$k(-x) = 8(-x)^3 + 3(-x) = -8x^3 - 3x$

Step3: Compare $k(-x)$ and $-k(x)$

We know $-k(x) = -8x^3 - 3x$, so $k(-x) = -k(x)$.

Step4: Classify the function

A function is odd if $k(-x) = -k(x)$.

Answer:

(c) $k(-x) = -k(x)$
(d) odd