The range of the function $f(x)=\frac{x-3}{5-x}, x \neq 5$ is

The range of the function $f(x)=\frac{x-3}{5-x}, x \neq 5$ is
  1. $\mathrm{R}-\{1\}$
  2. $\mathrm{R}-\{-5\}$
  3. $\mathrm{R}-\{5\}$
  4. $\mathrm{R}-\{-1\}$

Solution

We have $y=\frac{x-3}{5-x}$ $\therefore 5 y-x y=x-3 \Rightarrow x+x y=5 y+3$ $\therefore x=\frac{5 y+3}{1+y}$ Hence Range $=R-\{-1\}$

Asked in: MHT CET 2020 (19 Oct Shift 2)

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