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).
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.
Once the OP has settled the answer to his/her original question:
Let [itex]x = \frac{1}{2} + y[/itex]. In terms of y is the function [itex]g(y) = f(1/2+y)[/itex] 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).
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