If f(x) = 3x² and g(x) = 2x², what is f(g(x))?

To find f(g(x)), we first need to substitute g(x) into f(x). Given the functions:

• f(x) = 3x²
• g(x) = 2x²

Now, let’s substitute g(x) into f(x):

f(g(x)) = f(2x²)

Now, replace x in f(x) with 2x²:

f(g(x)) = 3(2x²)²

Next, we calculate (2x²)²:

(2x²)² = 4x⁴

Now, we substitute this back into the equation:

f(g(x)) = 3(4x⁴) = 12x⁴

Therefore, the final result is:

f(g(x)) = 12x⁴