Odd or Even: f(x)=6x(1-x)

[hofoen]

Is this function odd or even:
$$f(x) = 6x(1-x)$$

 

[CompuChip]

If it is odd, then f(-x) = -f(x)
If it is even, then f(-x) = f(x).
You can check which one it satisfies.
Note that it can be neither (i.e. if it is not odd, that doesn't necessarily mean it's even).

 

[n.karthick]

Another approach is, you can plot your function as a graph for different values of x say from -10 to 10. Now you see the graph of f(x) , whether it is symmetrical about y axis. If you see mirror image of function about y-axis it is even function and if you see negative reflection it is odd and if it is neither, then it is neither even nor odd function.

 

[uart]

Is this function odd or even.

No, it isn't.

 

[Mute]

Once the OP has settled the answer to his/her original question:

Let $x = \frac{1}{2} + y$. In terms of y is the function $g(y) = f(1/2+y)$ even or odd?

(Note that this does not really mean that f(x) is even or odd if g(y) is even or odd, since technically speaking f and g are not the same function, even though they are just the translations of each other).

 

[HallsofIvy]

Hofoen, please note that a function can be even or odd or neither or both.

That iws uart's point!