Find \((f\circ g)(-3)\)

📝 Question

Let:

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

Find \((f\circ g)(-3)\).

✅ Solution

🔹 Step 1: Use definition of composite function

\[ (f\circ g)(x)=f(g(x)) \] —

🔹 Step 2: Find \(g(-3)\)

\[ g(-3)=(-3)^2+1=9+1=10 \] —

🔹 Step 3: Find \(f(g(-3))\)

\[ f(10)=(10+1)^2=11^2 \] :contentReference[oaicite:0]{index=0} —

🎯 Final Answer

\[ \boxed{(f\circ g)(-3)=121} \]

🚀 Exam Shortcut

• First apply inner function \(g\)
• Then apply outer function \(f\)
• Follow order carefully: \(f(g(x))\)