[DRAFT] Functions


A function assigns a number to each number in its domain. The domain basically is all the numbers that can be plugged in or makes sense. For example for function f(x) = 1/x, x can not be 0 because division over 0 is not defined.

A function can not be ambiguous, for example B(x) = "some arrangement of the digits of x". The output for B(123) can be 123, 321, 231 and more. B(x) is not a function.

Two function are the same if they have produce the same output for the same input and have the same domain. f(x) = (1 + x)^2 and g(x) = x^2 + 2x + 1 are the same.

m(x) = x^2/x and n(x) = x are not the same because m(x) does not make sense when x is '0'. By the way n(x) = x is the identity function and t(x) = c is a constant function.

f(x) = sqrt(x) is also ambiguous. For example

f(9) = 3 and -3, this is not a function.