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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