Question

Which of the following is an odd function? f(x) = x3 + 5x2 + x mc023-1.jpg f(x) = x2 + x f(x) = –x

Answer 1

Given the functions
(a) f(x) = x³ + 5x² + x
(b) f(x) = x² + x
(c) f(x) = -x

Function (a)
f(-x) = (-x)³ + 5(-x)² + (-x)
       = -x³ + 5x² - x
       = -(x³ - 5x² + x)
The function is neither even nor odd.

Function (b)
f(-x) = (-x)² + (-x)
        = -(-x² + x)
The function is neither even nor odd.

Function (c)
f(-x) = -(-x)
       = x
       = -f(x)
Because f(-x) = -f(x) the function is odd.

Answer: f(x) = -x is an odd function.

Answer 2

By evaluating each function in -x, we will see that the only odd one is:

f(x) = -x

What is an odd function?

We say that a function is odd if:

f(-x) = f(x)

Then we just need to check that for the given functions, let's see what we get:

1) f(-x) = (-x)^3 + 5*(-x)^2 + (-x) = -x^3 + 5x^2 - x ≠ -f(x)

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

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

So the only odd function is the third one, one useful thing that you may need to know is that usually when you see even exponents, that function will not be odd.

If you want to learn more about odd functions, you can read:

https://brainly.com/question/1561362