Write the domain and range of the function f(x)= x-2 2-x - Vidyadip

Question

Write the domain and range of the function $\text{f(x)}=\frac{\text{x}-2}{2-\text{x}}$

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Answer

We have, $\text{f(x)}=\frac{\text{x}-2}{2-\text{x}}$ Domain of f, Clearly, f(x) is defined for all $\text{x}\in\text{R}$ except for which, $2-\text{x}\neq0\text{ i.e., x}\neq2$ Hence, domain (f) = R - {2} Range of f, Let f(x) = y $\Rightarrow\ \frac{\text{x}-2}{2-\text{x}}=\text{y}$ $\Rightarrow\ \frac{-1(2-\text{x})}{2-\text{x}}=\text{y}$ $\Rightarrow-1=\text{y}$ $\Rightarrow\text{y}=-1$ $\therefore\ \text{Range(f)}=\{-1\}$

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