Find the domain and range of the following real valued functions:… - Vidyadip

Question

Find the domain and range of the following real valued functions: $\text{f(x)}=\frac{\text{x}-2}{2-\text{x}}$

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Answer

Given, $\text{f(x)}=\frac{\text{x}-2}{2-\text{x}}$ Domain(f): Clearly, f(x) is defined for all x satisfying, if $2-\text{x}\neq0$ $\Rightarrow\ \text{x}\neq2$ Hence, domain (f ) = R - {2}. Range of f, Let f(x) = y $\Rightarrow\ \frac{\text{x}-2}{2-\text{x}}=\text{y}$ ⇒ x - 2 = y(2 - x) ⇒ x - 2 = - y(x - 2) ⇒ y = - 1 Hence, range (f) = {-1}.

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