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