Let and . If is a function defined by then show that is a one-one and an onto function.

Mathematics20232 marksDerivation

Let $A = \mathbb{R} - \{2\}$ and $B = \mathbb{R} - \{1\}$. If $f : A \to B$ is a function defined by $f(x) = \frac{x - 1}{x - 2}$ then show that $f$ is a one-one and an onto function.

Given: f : A \to B \text{ defined by } f(x) = \frac{x - 1}{x - 2}