Check if a function is one-one and onto

Chapter 1 Relations and Functions Class 12 Maths

Question. Let A = R – {3} and B = R – {1}. Consider the function {\displaystyle f: A \rightarrow B } defined by {\displaystyle f(x) = \frac{x-2}{x-3} } . Is f one-one and onto? Justify your answer.

equivalence-relations-and-equivalence-classes 06:11

Equivalence Relations and Equivalence Classes

A relation R on set A is said to be reflexive if (a, a) ∈ R, ∀ a ∈ A or aRa,∀a ∈ A symmetric if(a, b) ∈ R ⇒ (b, a) ∈ R, ∀ a, b ∈ A or aRb ⇒ bRa,∀ a, b ∈ A transitive if (a, b) ∈ R, (b, c) ∈ R ⇒ (a, c) ∈ R, ∀ a, b, c ∈ A or aRb and bRc ⇒ aRc ,  ∀ a, b, c ∈ A If a relation is reflexive, symmetric and transitive then the relation is said to be equivalence relation.