Question

if \\(f(x) = 3x^2\\) and \\(g(x) = 4x^3 + 1\\), what is the degree of \\((f \circ g)(x)\\)?

2
3
5
6

Explanation:

Express the composite function

$$ (f \circ g)(x) = f(g(x)) = 3(4x^3 + 1)^2 $$

Expand the expression to find the leading term

$$ (f \circ g)(x) = 3(16x^6 + 8x^3 + 1) = 48x^6 + 24x^3 + 3 $$

Determine the degree of the polynomial

$$ \text{Degree} = 6 $$

Answer:

• 2
• 3
• 5
• 6 (Correct answer)