Question

What type of function is g(x)=x−−√3
𝑔
(
𝑥
)
=
𝑥
3
?(1 point)
Responses

both even and odd
both even and odd

neither even nor odd
neither even nor odd

even
even

odd

Answer 1

To determine the type of function \( g(x) = x^{\frac{1}{3}} \) (the cube root of \( x \)), we need to check for evenness and oddness.

1. **Even Function**: A function \( f(x) \) is even if \( f(-x) = f(x) \) for all \( x \).
2. **Odd Function**: A function \( f(x) \) is odd if \( f(-x) = -f(x) \) for all \( x \).

Let's check \( g(x) \):

1. Calculate \( g(-x) \):
\[
g(-x) = (-x)^{\frac{1}{3}} = -x^{\frac{1}{3}} = -g(x)
\]

Since \( g(-x) = -g(x) \), it satisfies the condition for being an odd function.

Thus, the correct classification for the function \( g(x) = x^{\frac{1}{3}} \) is **odd**.

So, the response is:

**odd**