Question

Let A = R - {3} and B = R - {1}. Consider the function f:A→B defined by f(x)=(x-2/x-3).  Show that f is one-one and onto and hence find f ^-1 . 

Answer 1

Let x₁ , x₂ ∈A.
Now, f(x₁) = f(x₂ )

Hence f is one-one function.
For Onto

From above it is obvious that ∀y except 1,