Final answer:
To find g(f(3)), we first find the value of f(3) by substituting x = 3 into f(x) = 5x - 3, which gives us f(3) = 12. Then, we substitute f(3) = 12 into g(x) = x² - x + 5 to find g(f(3)) = 137.
Step-by-step explanation:
To find g(f(3)), we need to first find the value of f(3) and then use that result to find g(f(3)). Let's start by finding f(3). We are given that f(x) = 5x - 3, so substituting x = 3, we have f(3) = 5(3) - 3 = 15 - 3 = 12.
Now that we have f(3) = 12, we can use this value to find g(f(3)). We are given that g(x) = x² - x + 5, so substituting x = f(3) = 12, we have g(f(3)) = (12)² - 12 + 5 = 144 - 12 + 5 = 137.
Therefore, g(f(3)) = 137.