**Question:**

Mark (√) against the correct answer in the following:

Let $A=R-\{3\}$ and $B=R-\{1\} .$ Then $f: A \rightarrow A: f(x)=\frac{(x-2)}{(x-3)}$ is

A. one - one and into

B. one - one and onto

C. many - one and into

D. many - one and onto

**Solution:**

$\mathrm{f}: \mathrm{A} \rightarrow \mathrm{A}: \mathrm{f}(\mathrm{x})=\frac{(\mathrm{x}-2)}{(\mathrm{x}-3)}$

In this function

$x=3$ and $y=1$ are the asymptotes of this curve and these are not included in the functions of the domain and range respectively therefore the function $f(x)$ is one one sice there are no different values of $x$ which has same value of $y$.

and the function has no value at $y=1$ here range $=$ codomain

$\therefore f(x)$ is onto

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