if f(x) = f(-x), then the function is even. So, f(-x) = 2^-x which does not equal 2^x.
However, if f(-x) = -f(x), then the function is odd. So -f(x) = -2^x which does not equal f(-x) = 2^-x.
f(x) = 2^x is neither even nor odd.
A function that is even has the y axis (x=0) as an axis of symmetry f(x)=f(-x)
A function that is odd has point symmetry about the origin. This means that if it is rotated 180 degrees it will be the same. f(-x)=-f(x)
This is what 2x looks like. You can see that it is not symmetrical about the y axis.
And it does not have point symmetry about (0,0)
so it is not an even function or an odd function.
Let me add one thing to what Melody is saying......we can always "test" whether a function is even by replacing x with -x.....if the reults are the same, then the function is even.
Then, is 2(x) = 2(-x) ???........NO !!!
Note that a function like x2 is even, because...
x2 = (-x)2
And this is exactly what Melody said......
Aziz had already done that but perhaps your working is a bit clearer.
I saw that after I had posted...let me give Aziz full credit too!! (I won't take any points for my repeated answer!!.......)