How do you find the composition of the functions f(x) = 4x + 7 and g(x) = 10x + 6, denoted as f(g(x))?

To find the composition of the functions f and g, denoted as f(g(x)), we will substitute the expression of g(x) into the function f(x).

Given the functions:

We will start by calculating the value of g(x):

Now, we need to substitute g(x) into f(x):

So, f(g(x)) = f(10x + 6). This means we will replace every instance of x in f(x) with 10x + 6:

f(g(x)) = 4(10x + 6) + 7

Next, we will simplify this expression:

Thus, the composition of the functions f and g, or f(g(x)), is:

f(g(x)) = 40x + 31

This resulting function represents the process of taking the output of g and using it as the input for f.