Question

given (f(x) = x + 1), (g(x) = 2x), (h(x) = x^3)

what is ((f \circ g \circ h)(x))?

• (2x^3 + 1)
• (8x^3 + 9x + 1)
• (8x^3 + 12x^2 + 6x + 1)
• (8x^3 + 24x^2 + 24x + 8)

Explanation:

⚡ Using what you learned: Evaluating Composite Functions

Step 1: Define the composition

$$ (f \circ g \circ h)(x) = f(g(h(x))) $$

Step 2: Substitute \( h(x) \) into \( g(x) \)

$$ g(h(x)) = g(x^3) = 2(x^3) = 2x^3 $$

Step 3: Substitute the result into \( f(x) \)

$$ f(g(h(x))) = f(2x^3) = 2x^3 + 1 $$

Answer:

\( 2x^3 + 1 \)