Question

Which of the is an odd function

Answer 1

g(x) = 4x.

Explanation:

If f(-x) = f(x) the function is even.

If f(-x) = -f(x) then the function is odd.

x^2: g(x) == x^2 and g(-x) = x^2 so this is even.

5x - 1: g(x) = 5x - 1 . g(-x) = -5x - 1 = -(5x + 1) so this is nether odd nor even.

3: neither even nor odd.

4x: g(x) = 4x , g(-x) = -4x = -g(x) so this is ODD.

Answer 2

g(x) = 4x

Explanation:

Recall by definition that for an odd function g

g(-x) = - g(x)

to identify the odd fuction, we simply replace each "x" with "-x" and see which results in the negative of the original function. The only choice that will give you this result is Option 4

Option 4:

g(x) = 4x

g(-x) = 4(-x) = -4x [which is equal to -g(x), hence this is an odd function]

In contrast, (and for a sanity check) let's try option 1

Option 1:

g(x) = x²

g(-x) = (-x²) = x² ( ≠ -g(x) , hence not an odd function)