Find \((f\circ g)(-2)\)

📝 Question

Let:

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

Find \((f\circ g)(-2)\).

✅ Solution

🔹 Step 1: Use definition

\[ (f\circ g)(x)=f(g(x)) \] —

🔹 Step 2: Find \(g(-2)\)

\[ g(-2)=1-(-2)^2=1-4=-3 \] —

🔹 Step 3: Find \(f(g(-2))\)

\[ f(-3)=(-3)^2+(-3)+1 \] :contentReference[oaicite:0]{index=0} —

🎯 Final Answer

\[ \boxed{(f\circ g)(-2)=7} \]

🚀 Exam Shortcut

• Compute inner function first
• Then substitute into outer function
• Careful with signs