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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions2 Marks
MCQ
If $f: R-\{2\} \rightarrow R$ is a function defined by $f(x)=\frac{x^2-4}{x-2}$, then its range is
  • A
    $R$
  • B
    $R-\{2\}$
  • ✓
    $R=\{4\}$
  • D
    $R=\{-2,2\}$
✓

Answer

Correct option: C.
$R=\{4\}$
(c): We have, $y=f(x)=\frac{x^2-4}{x-2}, x \neq 2$ $=\frac{(x-2)(x+2)}{x-2}=x+2, x \neq 2$.
It follows from the above relation that $y$ take all real values except when $x$ takes values in the set $R-\{2\}$
$\therefore \quad$ Range $(f)=R-\{4\}$

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