Q) Let A = R – {5} and B = R – {1}. Consider the function f: A → B, defined by f(x) = (𝑥−3)/

Q) Show that a function 𝑓:𝑅_+→𝐴⊂𝑁, defined as 𝑓(𝑥)=4𝑥^2+12𝑥+15 is one-one. Find gset 𝐴

Q) Show that a function f: R → R defined by f(x) = 2𝑥/(1+𝑥^2 ) is neither one-one nor onto.

🚨 COMPOSITE FUNCTION PROOFS LOOK HARD… UNTIL YOU SEE THIS METHOD! Most students get stuck on “Show that…” questions because: ❌ They don’t know where to start ❌ They mix up (f(g(x))) and (g(f(x))) ❌ They expand correctly but can’t reach the given answer So they panic… and lose EASY marks in the exam. But here’s the trick 👇 In composite function proofs, the goal is to work step-by-step until your algebra matches the answer they gave you. In this lesson, I show you: ✅ How to substitute one functi