Which Of The Following Funtion is neither even or odd function?

Question

Which of the following function is neither even nor odd function?
f(x) = -|x2| + 2
f(x) = x3 + 3x
f(x) = -x2 + |x|
f(x) = -x3 + |x|

Answer 1

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

 

If f(x) = -x³ + lxl, then f(-x) = -(-x)³+l-xl = x³+lxl ≠ f(x) (f is not even)

 

                                                                     ≠ -f(x) (f is not odd)

 

So, f(x) = -x³ + lxl is neither even nor odd.  

Answer 2

A function is even if   f(-x) = f(x),        A parabola is a good example of this.  This is because a parabola has an axis of symmetry.  Otherwise, function is odd.

 

 

Use the following definition I provided here to find that function that is neither even or odd.