Find \((f\circ g)(7)\)

📝 Question

Let:

\[ f(x)=x+7,\quad g(x)=x-7 \]

Find \((f\circ g)(7)\).

✅ Solution

🔹 Step 1: Use definition

\[ (f\circ g)(x)=f(g(x)) \] —

🔹 Step 2: Find \(g(7)\)

\[ g(7)=7-7=0 \] —

🔹 Step 3: Find \(f(g(7))\)

\[ f(0)=0+7=7 \] —

🎯 Final Answer

\[ \boxed{7} \]

🚀 Exam Shortcut

• Compute inner function first
• Then apply outer function
• Here: \(g(7)=0 \Rightarrow f(0)=7\)