Question

Math question 13 help

Answer 1

This is an odd function

Explanation:

Given a function f(x),

if f(-x) = f(x) then the f(x) is even
If f(-x) = -f(x0 then the function is odd

If neither of the above is true then the function is neither odd nor even

We are given

`f(x) = 4x^3 - x^5 + 5x\\f(-x) = 4(-x)^3 -(x)^5 + 5(-x)\\\\(-x)^3 = - x^3\\(-x)^5 = -x^5\\\\\\\therefore\\f(-x) = 4(-x^3) - (-x^5) + 5 (-x)\\\\= -4x^3 + x^5 - 5x\\\\= -(4x^3 -x^5 + 5x)\\\\= -f(x)`

So the function is odd