How do you find the composition of the functions f(x) = 5x + 4 and g(x) = 6x + 7?

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To find the composition of the functions f(x) = 5x + 4 and g(x) = 6x + 7, we need to determine what f(g(x)) looks like. This means we’ll substitute the entire function g(x) into the function f(x).

Here’s a step-by-step breakdown:

  1. Start with g(x):

    2. g(x) = 6x + 7

  2. Now substitute g(x) into f(x):

    3. We will replace x in f(x) with g(x):

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

  3. Substituting the expression of g(x) into f(x):

    4. f(g(x)) = 5(6x + 7) + 4

  4. Now simplify this expression:

    5. First, distribute the 5:

    f(g(x)) = 30x + 35 + 4

    Next, combine the constants:

    f(g(x)) = 30x + 39

So, the final result is:

f(g(x)) = 30x + 39

This result represents the composition of the two functions, which combines the effects of both f(x) and g(x) into a new function.

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