Gujarat BoardEnglish MediumSTD 11 CommerceStatisticsFunction2 Marks
Question
$f: Z-\{2\} \rightarrow Z, f(x)=\frac{x^2+x-6}{x-2}$, State the type of the function.
✓
Answer
$f: Z-\{2\} \rightarrow Z$
$\therefore$ Domain $=\{\ldots-3,-2,0,1,2,3,4, \ldots\}$
$f(x)=\frac{x^2+x-6}{x-2}$,
$\therefore f(-3)=\frac{9-3-6}{-3-2}=\frac{0}{-5}=0$
$f(-2)=\frac{4-2-6}{-2-2}=1$
$f(-1)=\frac{1-1-6}{-1-2}=2$
$f(0)=\frac{-6}{-2}=3$
$f(1)=\frac{1+1-6}{1-2}=\frac{-4}{-1}=4$
$f(3)=\frac{9+3-6}{3-2}=6$
$f(4)=\frac{16+4-6}{4-2}=\frac{14}{2}=7$
Here, for two different elements of domain, their images are not same. Therefore, the given function is one - one function.
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