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

Question

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

✓

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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