What is the composition of the functions g(x) and f(x) given their definitions as f(x) = 5x + 1 and g(x) = 3x + 9?

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

Given:

  • f(x) = 5x + 1
  • g(x) = 3x + 9

Now, we will compute g(f(x)):

  1. First, we need to replace x in g(x) with f(x):
    2. g(f(x)) = g(5x + 1)
  2. Next, substitute f(x) into g(x):
    3. g(5x + 1) = 3(5x + 1) + 9
  3. Now, we distribute the 3:
    4. g(5x + 1) = 15x + 3 + 9
  4. Finally, we combine like terms:
    5. g(5x + 1) = 15x + 12

Thus, the composition g(f(x)) is:

g(f(x)) = 15x + 12

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