Question

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

odd
odd

neither even nor odd
neither even nor odd

both even and odd
both even and odd

even

Answer 1

To determine whether the function \( g(x) = \sqrt{x}^3 \) is even, odd, or neither, we analyze the function by checking \( g(-x) \).

1. **Evaluating \( g(x) \)**:
\( g(x) = \sqrt{x}^3 \)

2. **Evaluating \( g(-x) \)**:
Since the square root function is not defined for negative numbers in the reals, we have:
- If \( x \) is positive, \( g(-x) \) is undefined.
- If \( x \) is negative, \( g(x) \) is also undefined.

Because the function is not defined for negative \( x \), we cannot establish relationships that would classify the function as even or odd.

### Conclusion:
The correct response is: **neither even nor odd**.