MHT CET · Maths · Functions
The range of the function \(f(x)=\frac{x-3}{5-x}, x \neq 5\) is
- A \(\mathrm{R}-\{1\}\)
- B \(\mathrm{R}-\{-5\}\)
- C \(\mathrm{R}-\{5\}\)
- D \(\mathrm{R}-\{-1\}\)
Answer & Solution
Correct Answer
(D) \(\mathrm{R}-\{-1\}\)
Step-by-step Solution
Detailed explanation
(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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