Question

Let $A = \mathbb{R} - \{3\}$ and $B = \mathbb{R} - \{1\}$. A function $f : A \to B$ is defined by $f(x) = \frac{x - 2}{x - 3}$. Find whether $f$ is one-one and onto.

Hint:

Any linear fractional function of the form $f(x) = \frac{ax+b}{cx+d}$ is always one-one on its natural domain, provided that its determinant condition $ad - bc \neq 0$ is satisfied. Here, $(1)(-3) - (-2)(1) = -1 \neq 0$.

Answer 1