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
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.
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.
For all x not equal to 0, -x/x = -1
The x coordinate for all y intercepts is 0, just as the y coordinate for all x intercepts is 0.
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.
All real numbers.
No. Not all functions are continuous. For example, the function f(x) = 1/x is undefined at x = 0.
YES, all linear equations have x-intercepts. because of the x, y has to be there 2!
The properties of multiplication need to be considered in the context of the set over which this operation is defined.For most number systems, multiplications isCommutative: x*y = y*x for all x and yAssociative: (x*y)*z = x*(y*z) so that , without ambiguity the expression can be written as x*y*z for all x, y and zDistributive property over addition or subtraction:x*(y+z) = x*y + x*z for all x, y and zIdentity Element: There exists a unique element, denoted by 1, such that1*x = x = x*1 for all xZero element: there is an element 0, such that x*0 = 0 for all x.In some sets, an element x also has a multiplicative inverse, denoted by x-1 such that x*x-1 = x-1*x = 1 (the identity).
tan(-x) = -tan(x)