Find \(f\circ g\)

📝 Question

Let:

\[ f=\{(5,2),(6,3)\}, \quad g=\{(2,5),(3,6)\} \]

Find \(f\circ g\).

✅ Solution

🔹 Step 1: Definition

\[ (f\circ g)(x)=f(g(x)) \] —

🔹 Step 2: Apply \(g\) first

\[ g(2)=5,\quad g(3)=6 \] —

🔹 Step 3: Apply \(f\)

\[ f(5)=2,\quad f(6)=3 \] —

🔹 Step 4: Write composition

\[ (f\circ g)(2)=2,\quad (f\circ g)(3)=3 \]

So,

\[ f\circ g=\{(2,2),(3,3)\} \] —

🎯 Final Answer

\[ \boxed{f\circ g=\{(2,2),(3,3)\}} \]

🚀 Exam Shortcut

• First apply \(g\), then \(f\)
• Follow arrows carefully
• Write final ordered pairs clearly