Final answer:
To find the value of f(x), substitute g(x) into the equation (gof)(x) = 2x + 5 and solve for f(x). The value of f(x) is (2/5)x + 2/5.
Step-by-step explanation:
To find the value of f(x), we need to solve (gof)(x) = 2x + 5. We know that g(x) = 5x + 3, so we can substitute this into the equation. (gof)(x) = g(f(x)) = 2x + 5.
Substituting g(x) = 5x + 3, we get 5f(x) + 3 = 2x + 5.
Next, we solve for f(x).
Subtracting 3 from both sides of the equation, we obtain 5f(x) = 2x + 2. Dividing both sides by 5, we get f(x) = (2/5)x + 2/5.
Therefore, the value of f(x) is (2/5)x + 2/5.