Question

f(x) = x + 9, g(x) = x^2 - 4x, h(x) = x^4 + 2x^3

what is the degree of (f \circ g \circ h)(x)?

• 7
• 8
• 21
• 24

Explanation:

⚡ Using what you learned: Evaluating Composite Functions

Step 1: Identify individual degrees

Identify the degree (the highest exponent of \( x \)) for each polynomial function:

• For \( f(x) = x + 9 \), the degree is \( 1 \).
• For \( g(x) = x^2 - 4x \), the degree is \( 2 \).
• For \( h(x) = x^4 + 2x^3 \), the degree is \( 4 \).

Step 2: Apply the degree rule for composition

When composing polynomial functions, the degree of the composite function is the product of the degrees of the individual functions:

$$ \text{Degree of } (f \circ g \circ h)(x) = \text{deg}(f) \times \text{deg}(g) \times \text{deg}(h) $$

Step 3: Calculate the final degree

Multiply the degrees together:

$$ 1 \times 2 \times 4 = 8 $$

Answer:

8