# Composition of functions

If we have two or more functions that are contained within each other, we call it compound functions. Its general expression is as follows: The value of the compound function in x is equal to the function f evaluated in g (x). ## Definition

Given two functions f and g, the composite function of f with g is defined as: his domain is the set of all x (variable) that are in the domain of g, such that g (x) belongs to the domain of f. That is to say: Exercise 1: Sean: y Determine:

1. We know that: We first substitute the value of g (x): Now, to evaluate f, we substitute x = g (x): We simplify: We solve the binomial:   To determine the domain we must remember that: We will first look for the domain of g (x); Since the function has a root and the variable is inside it, it cannot be negative:  Then the domain of g will be all values greater than or equal to four, that is: For the domain of f: since its function is a polynomial, it will be all real numbers, that is: Since we are looking for the domain of the compound function, we know that this domain depends directly on g (x), therefore: 