JEE Main 2022 (Online) 25th July Evening ShiftQuestion 1
The sum of the maximum and minimum values of the function $f(x)=|5x-7|+[x^2+2x]$ in the interval $\left[\frac54,2\right]$, where $[t]$ is the greatest integer $\le t$, is ________.
Sets, Relations and Function
Answer$15$
Solution
On $[5/4,2]$: $5x-7$ changes sign at $7/5$. $g(x)=[x^2+2x]$ is nondecreasing; $x^2+2x$ ranges $4.0625\to8$, so $g\in\{4,\dots,8\}$. At $x=7/5$: $0+[4.76]=4$ is the minimum (term 1 is $\ge0$, $g\ge4$). At $x=2$: $3+8=11$; just below 2: $\approx3+7=10$; so max is 11. Sum $=4+11=15$.