Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
The range of the function $f(x)=\frac{x^2-3 x+2}{x^2+x-6}$ is
A
$R -\left[\frac{1}{5}, 1\right]$
B
R
✓
$R -\{1\}$
D
$R-\{-3,2\}$
✓
Answer
Correct option: C.
$R -\{1\}$
(C) $f (x)$ is defined for $x^2+x-6 \neq 0$, i.e., $x \neq-3,2$ $\therefore \quad \operatorname{Dom}(f)=R-\{-3,2\}$ Let $y=\frac{x^2-3 x+2}{x^2+x-6}=\frac{x-1}{x+3}$ $\Rightarrow x-\frac{3 y+1}{y-1}$ $x$ is real for $y-1 \neq 0$, i.e., $y \neq 1$ Hence, $\operatorname{range}(f)=R-\{1\}$
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