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