Question

Which of the following functions are odd?

Answer 1

1,23

Explanation:

Answer 2

Option 1, 2 and 3

Explanation:

A function f(x) is odd if f(-x) = -f(x).

The graphs of odd functions are symmetric with the origin.

It is also known that the sum of two odd functions results in an odd function, so the third option is an odd function.

The first option shown is:

`f(x) -x ^ 3 -x`

If we make f (-x) we are left with:

`f(-x) = - (-x ^ 3) - (-x)\\\\f(-x) = x ^ 3 + x = -f(x)`

The function is odd.

The second option is a graph that has rotational symmetry of 180 ° with respect to the origin, that's why it is odd function.

The rest of the options are not odd functions because it is not true that f(-x) = -f(x)

Option 1 and 2 and 3