Find \((f\circ f^{-1})(1)\)

📝 Question

Let:

\[ f:\mathbb{R}\to\mathbb{R}, \quad f(x)=\frac{2x-3}{4} \]

Find \((f\circ f^{-1})(1)\).

✅ Solution

🔹 Step 1: Key Property

If \(f\) is invertible, then:

\[ (f\circ f^{-1})(x)=x \] —

🔹 Step 2: Apply property

\[ (f\circ f^{-1})(1)=1 \] —

🎯 Final Answer

\[ \boxed{1} \]

🚀 Exam Shortcut

• \(f(f^{-1}(x))=x\)
• No need to find inverse explicitly
• Direct answer = input value