Question

Let $f\left(x\right)=\frac{x^2+2}{\left[x\right]},1\le x\le 3,$ where [.] denotes greatest integer function, then incorrect statement is

• A. $f\left(x\right)$ is increasing in $[1,3]$
• B. least value of $f\left(x\right)$ is 3
• C. $f\left(x\right)$has no greatest value
• D. domain of $f^{\prime }\left(x\right)$ is $(1,3)-\left\{2\right\}$

Answer 1

The correct option is A $f\left(x\right)$ is increasing in $[1,3]$

$f\left(x\right)=\{\begin{array}{cc}{x}^2+2& 1\le x<2\\ \frac{x^2+2}{2}& 2\le x<3\\ \frac{11}{3}& x=3\end{array}$