Which of the following is an odd function?

f(x) = -x is odd

Step-by-step explanation:

A function f is odd if f(-x) = -f(x) for all x in the domain of f. Then, let's check each of the functions.

1. f(x) = x^3 + 5x^2 + x

f(-x) = (-x)^3 + 5(-x)^2 + (-x) = -x^3 + 5x^2 - x

-f(x) = -(x^3 + 5x^2 + x) = -x^3 - 5x^2 - x

Given that f(-x) ≠ -f(x). The function f is not odd.

2. f(x) = sqrt(x)

f(-x) = sqrt(-x) (Imaginary number)

-f(x) = -sqrt(x)

Given that f(-x) ≠ -f(x). The function f is not odd.

3. f(x) = x^2 + x

f(-x) = (-x)^2 -x = x^2 - x

-f(x) = -x^2 - x

Given that f(-x) ≠ -f(x). The function f is not odd.

4. f(x) = -x

f(-x) = - (-x) = x

-f(x) = -(-x) = x

Given that f(-x) = -f(x). The function f is odd.