Question

f(x) = x^2 + 4 \quad g(x) = x - 5 \\\\
(f \circ g)(x) = ? \\\\
\circ \quad x^2 - 1 \\\\
\circ \quad x^2 - 21 \\\\
\circ \quad x^2 - 10x + 25 \\\\
\circ \quad x^2 - 10x + 29

Explanation:

⚡ Using what you learned: Evaluating Composite Functions

Step 1: Set up the composition

$$ (f \circ g)(x) = f(g(x)) = f(x - 5) $$

Step 2: Substitute and expand

$$ f(x - 5) = (x - 5)^2 + 4 $$

$$ f(x - 5) = (x^2 - 10x + 25) + 4 $$

$$ f(x - 5) = x^2 - 10x + 29 $$

Answer:

\( x^2 - 10x + 29 \)