What kind of function is f(x) = 4x^2 - 2x, odd, even, neither, both.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

A function f(x) is even if f(x) = f(-x); and it is odd if f(-x) = -f(x).

To determine if f(x) is odd, even or neither substitute x with -x in the given function and notice what happens.

f(-x) = 4*(-x)^2 - 2*(-x)

= 4x^2 + 2x

`4x^2 + 2x != 4x^2 - 2x`

and `4x^2 + 2x != -(4x^2 - 2x)`

The function f(x) = 4x^2 - 2x is neither even nor is it odd.

sciencesolve's profile pic

sciencesolve | Teacher | (Level 3) Educator Emeritus

Posted on

You need to test the parity of function by replacing -x for x in equation of function, such that:

`f(-x) = 4*(-x)^2 - 2*(-x)`

`f(-x) = 4x^2 + 2x`

Since `f(-x)!=f(x)` and `f(-x)!=-f(x)` , hence, the function is neither even, nor odd.

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