Question

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

• A. $\{x:x\in R,x<3|$
• B. $\{x:x\in R,x\ne 3\}$
• C. $\{x:x\in R|$
• D. $\{x:x\in R,x\ne 2,x=-3\}$

Answer 1

The correct option is B $\{x:x\in R,x\ne 3\}$

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

$=\frac{x^2-2x-x+2}{x^2+3x-2x-6}$

$=\frac{x(x-2)-(x-2)}{x(x+3)-2(x+3)}$

$=\frac{(x-2)(x-1)}{(x+3)(x-2)}$

$=\frac{(x-1)}{(x+3)}$

Domain of $f\left(x\right)$ is $\{x:x\in R,x\ne -3\}$