Question

Domain of function as $f\left(x\right)=\frac{{}^3\sqrt{x^2-5x+6}}{x^2-x-6}$ is

• A. $\left[2,3\right]$
• B. $R-\left\{-3,2\right\}$
• C. $R-\left\{-2,3\right\}$
• D. $R$

Answer 1

The correct option is C $R-\left\{-2,3\right\}$

$f\left(x\right)=\left(\frac{\sqrt[3]{3x^2-5x+6}}{x^2-x-6}\right)$

$Cuberootexpressionisfineforanyvalueoftheterminsidetheroot.$

$Butthedenomiantormustnotbeequaltozero.$

$x^2-x-6\ne 0$

$(x-3)(x+2)\ne 0$

$x\ne 3orx\ne -2$

$\therefore$ domain: R- {-2,3}