Show that the function `f: R-{3}->R-{1}` given by `f(x)=(x-2)/(x-3)` is bijection.

Explanation

To show that the function \( f: \mathbb{R} - \{3\} \to \mathbb{R} - \{1\} \) given by \( f(x) = \frac{x-2}{x-3} \) is a bijection, we need to prove that it is both one-to-one (injective) and onto (surjective).

### Step 1: Prove that \( f \) is one-to-one (injective)

To prove that \( f \) is one-to-one, we assume that \( f(x_1) = f(x_2) \) for some \( x_1, x_2 \in \mathbb{R} - \{3\} \). This means:

\[
\frac{x_1 - 2}{x_1 - 3} = \frac{x_2 - 2}{x_2 - 3}
...