How do you find f of g(x) if f(x) = 4x + 7 and g(x) = 3x^2?

Finding f(g(x))

To find f(g(x)), we need to substitute g(x) into the function f(x). Let’s break this down step by step:

Step 1: Define the functions

We have two functions:

• f(x) = 4x + 7
• g(x) = 3x²

Step 2: Substitute g(x) into f(x)

Now, we’ll substitute g(x) into f(x):

f(g(x)) = f(3x2)
    

Step 3: Compute f(3x²)

Now, replace every instance of x in f(x) with 3x²:

f(3x2) = 4(3x2) + 7
    

Step 4: Simplify

Perform the multiplication and addition:

f(3x2) = 12x2 + 7
    

Conclusion

Therefore, the final result for f(g(x)) is:

f(g(x)) = 12x² + 7