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If f(x) = x 2 + 1 and g(x) = 3x + 1, find 2f(1) + 3g(4).

Question

If f(x) = x 2 + 1 and g(x) = 3x + 1, find 2f(1) + 3g(4).

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Solution

Sure, let's solve this step by step:

  1. First, we need to find the values of f(1) and g(4).
  2. Substitute x = 1 into the function f(x) = x^2 + 1. This gives f(1) = 1^2 + 1 = 2.
  3. Substitute x = 4 into the function g(x) = 3x + 1. This gives g(4) = 3*4 + 1 = 13.
  4. Now, substitute f(1) and g(4) into the expression 2f(1) + 3g(4). This gives 22 + 313 = 4 + 39 = 43.

So, 2f(1) + 3g(4) = 43.

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