Injective:

An injective function or injection or one-to-one function is a function that preserves distinctness: it never maps distinct elements of its domain to the same element of its codomain. In other words, every element of the function's codomain is the image of at most one element of its domain.

Surjective:

A function f from a set X to a set Y is surjective (or onto), or a surjection, if every element y in Y has a corresponding element x in X such that f(x) = y. (It is not required that x is unique; the function f may map one or more elements of X to the same element of Y.)

Bijective:

A bijection, bijective function or one-to-one correspondence is a function between the elements of two sets, where each element of one set is paired with exactly one element of the other set, and each element of the other set is paired with exactly one element of the first set. There are no unpaired elements. In mathematical terms, a bijective function f: X → Y is a one-to-one (injective) and onto (surjective) mapping of a set X to a set Y.

Problem:

1. f o g o f

   $f(g(f(x)))=f(g(x+2))=f((x+2)^2)= (x+2)^2+2=x^2+2x+4+2=x^2+2x+6$

2. g o f o g

   $g(f(g(x)))=g(f(x^2))=g(x^2+2)= (x^2+2)^2$