Question

The function given by $f\left(x\right)=\frac{3x+7}{x^2-5x+6}$ is continuous in

• A. $(2,3]$
• B. $R-[2,3]$
• C. $R-\{2,3\}$
• D. None of the above

Answer 1

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

$f\left(x\right)$ is not defined when denominator equals $0$
So, for $f\left(x\right)$ to be continuous, $x^2-5x+6\ne 0,$
$\Rightarrow$ $x\ne 2,3$
So, $f\left(x\right)$ is continuous for all $x\in R-\{2,3\}$