Question

The domain of $\frac{x+1}{\sqrt{x^2-5x+6}}$ is

• A. R-{2,3}
• B. $(3,\infty )$
• C. $(-\infty ,\infty )$
• D. $(-\infty ,2)\cup (3,\infty )$

Answer 1

The correct option is A R-{2,3}

$\frac{x+1}{\sqrt{x^2-5x+6}}$

$x^2-5x+6>0$

$x^2-3x-2x+6>0$

$x(x-3)-2(x-3)>0$

$(x-3)(x-2)>0$

$x\in [-\infty ,2)\cup (3,\infty )$

Domain of

$x+1\in R$

$\therefore$ Domain of $\frac{x+1}{\sqrt{x^2-5x+6}}$ is $R-(2,3)$

Option $A=R-(2,3)$