How do you solve for fg(x) when f(x) is defined as x^4 and g(x) as 2x + 3, specifically for x = 2?

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To solve for fg(x) given the functions f(x) = x^4 and g(x) = 2x + 3, we need to follow a few steps:

  1. First, substitute x = 2 into the function g(x).
  2. Then, take the result from g(2) and substitute it into the function f(x) to find fg(2).

Step 1: Evaluate g(2)

Substituting x = 2 into g(x):

g(2) = 2(2) + 3 = 4 + 3 = 7

Step 2: Evaluate f(g(2)) = f(7)

Now we substitute g(2) = 7 into f(x):

f(7) = 7^4 = 2401

Final Result

Therefore, fg(2) = f(g(2)) = f(7) = 2401.

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