To find the expression equivalent to f(g(x)), we need to substitute g(x) into f(x).

Given:

• f(x) = 3x²
• g(x) = x² + 1

Now, we substitute g(x) into f(x):

f(g(x)) = f(x² + 1)

Substituting g(x) into f(x):

• f(g(x)) = 3(g(x))²
• = 3(x² + 1)²

Next, we need to expand (x² + 1)²:

• (x² + 1)² = (x²)² + 2(x²)(1) + (1)²
• = x⁴ + 2x² + 1

Now, we substitute this back into our expression:

f(g(x)) = 3(x⁴ + 2x² + 1)

Finally, distribute the 3:

• f(g(x)) = 3x⁴ + 6x² + 3

Thus, the expression equivalent to f(g(x)) is 3x⁴ + 6x² + 3.