I already answered this queston. This is the answer:
1) Relationship of input and output values for a composite function.
The composition of the functions p(x) compose with q(x) is defined as:
(p ° q) (x) = p [q(x) ]
That means that the output of the function q(x) is the input of the function p(x).
2) Is the inverse of a function always a function?
No, the inverse of a function is not always a function.
Remember that a function cannot have two different outputs for the same input.
Given tha tthe outputs of the original function are the inputs of the inverse function and the inputs of the original are the outputs of the inverse, if the original function has two or more inputs that result in a same output, when you inverse the original function, the latter would have some inputs related with more than one output, which is the negation of a function.
