not my
For an even function, f(-x) = f(x) for all x. For an odd function, f(-x) = -f(x) for all x.
Prove all x px or all x qx then all x px or qx
Yes!
If f(-x) = f(x) for all x then x is even. Example f(x) = cos(x). If f(-x) = -f(x) for all x then x is odd. Example f(x) = sin(x). In all other cases, f(x) is neither.
For all x not equal to 0, -x/x = -1
Equality is a binary relationship, defined on a set S, with the following properties:Reflexivity: x = x for all x in the set S.Symmetry: if x = y then y = x for all x, y in S.Transitivity: if x = y and y = z then x = z for all x, y and z in S.
The x coordinate for all y intercepts is 0, just as the y coordinate for all x intercepts is 0.
All real numbers.
As I understand the question: yes, f(x) can be a function even if f(x) is not defined for all x. For example, f(x) = x/x is a function that is equal to 1 everywhere but at x=0, where it is undefined.
No. Not all functions are continuous. For example, the function f(x) = 1/x is undefined at x = 0.
tan(-x) = -tan(x)
It is the additive identity. That is, x + 0 = x = 0 + x for all x.