<p>Let <strong>f(x) = 8x + 3</strong> and <strong>g(x) = x² + 4</strong>. Find <strong>(g∘f)(2)</strong>.</p>
Step-by-Step Solution
Key Concept: To find (g∘f)(x), first evaluate f(x), then apply g to that result.
<p><strong>Step 1:</strong> Calculate (g∘f)(2) = g(f(2))</p><p><strong>Step 2:</strong> Find f(2)</p><p>Using f(x) = 4x + 5: f(2) = 4(2) + 5 = 8 + 5 = 13</p><p><strong>Step 3:</strong> Find g(13)</p><p>g(13) = (13)² + 4 = 169 + 4 = 173</p><p><strong>Step 4:</strong> Therefore (g∘f)(2) = <strong>173</strong></p>
Correct Answer: 173