example of a composite function. Explain your variables how they're represented in the function, and which elem. functions are combined to form the composite function
You need to know that the process of composition of two functions is represented by the following notation(left) and the following result(right), such that:
`(fog)(x) = f(g(x))`
You should remember that if a problem requests to find the value of a function f(x), at a point x = a, you need to substitute a for x in equation of the function.
The same process works in composition of two function, thus, if the problem requests to find f(g(x)), you need to substitute g(x) for x in equation of f(x).
Since an worked example will make you better understand the process of composition, you may consider the following two functions, `f(x) = x^2` and `g(x) = 7x+5` .
You need to find `(fog)(x)` such that:
`(fog)(x) = f(g(x)) ` (first you need to write the result of composition)
`f(g(x))= (g(x))^2` (substitute g(x) for x in equation of f(x))
`f(g(x)) = (7x+5)^2` (replace g(x) with its equation)
`f(g(x)) = 49x^2 + 70x + 25` (raise the binomial to square using the formula `(a+b)^2 = a^2 + 2ab + b^2` )
Hence, evaluating the result of composition of the functions f(x) and g(x) yields `f(g(x)) = 49x^2 + 70x + 25` .
Thus, the compositions of functions use the rules of substitution, as it is shown in the previous example, hence `(fog)(x) = f(g(x)).`