Question

Domain of the function $f\left(x\right)=\frac{x^2-3x+2}{x^2+x-6}$ is

• A. {$x:xϵR,x\ne -3$}
• B. {$x:xϵR,x\ne 2$}
• C. {$x:xϵR$}
• D. {$x:xϵR,x\ne 2,x\ne -3$}

Answer 1

The correct option is D {$x:xϵR,x\ne 2,x\ne -3$}

Given,

$f\left(x\right)=\frac{x^2-3x+2}{x^2+x-6}$

$x^2+x-6=0$

roots of above equation are:

$x=-3,2$

So, $x$ can't be equal to $-3or2$

The above points are undefined

The function domain is

$x<-3,-3<x<2,x>2$

$\{x:x\in R,x\ne 2,x\ne -3\}$