Find \(g\circ f(x)\)

📝 Question

Let:

\[ f(x)=2x+1,\quad g(x)=x^2-2 \]

Find \(g\circ f(x)\).

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✅ Solution

🔹 Step 1: Use definition

\[ (g\circ f)(x)=g(f(x)) \] —

🔹 Step 2: Substitute \(f(x)\)

\[ g(f(x))=g(2x+1) \] —

🔹 Step 3: Apply function \(g\)

\[ g(2x+1)=(2x+1)^2-2 \] —

🔹 Step 4: Expand

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🎯 Final Answer

\[ \boxed{g\circ f(x)=4x^2+4x-1} \]

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🚀 Exam Shortcut

• Apply inner function first
• Substitute carefully
• Expand square properly