How to Find f(g(x)) for Given Functions f(x) and g(x)?

To find f(g(x)), we need to start by identifying the functions f(x) and g(x) based on the given information:

• f(x) = 4x + 6
• g(x) = 5x^2

Now, let’s break down the steps to perform the operations:

1. Step 1: Substitute g(x) into f(x). This means we will replace every instance of x in f(x) with g(x).
2. Step 2: Thus, we compute f(g(x)) = f(5x^2). Plugging 5x^2 into the function f(x):
3. f(5x^2) = 4(5x^2) + 6
4. Step 3: Simplify the expression:
5. f(5x^2) = 20x^2 + 6

So, the final result is:

• f(g(x)) = 20x^2 + 6

This process demonstrates how we can evaluate the composition of two functions and find f(g(x)).