Question

Let $\left[x\right]$ denote the greatest integer less than or equal to $x.$ If the domain of the function $\frac{1}{[x{]}^2-7[x]+12}$ is $R-[a,b),$ then the value of $a+b$ is

• A. $9$
• B. $8$
• C. $5$
• D. $15$

Answer 1

The correct option is B $8$

$\frac{1}{[x{]}^2-7[x]+12}$ is defined if
$[x{]}^2-7[x]+12\ne 0$
$\Rightarrow (\left[x\right]-3)(\left[x\right]-4)\ne 0$
$\Rightarrow \left[x\right]\ne 3$ and $\left[x\right]\ne 4$
$\Rightarrow x\notin [3,5)$
$\Rightarrow x\in R-[3,5)$
$\therefore a+b=3+5=8$