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  4. The sum of the maximum and minimum values of the function f(x)=|5 x-7|+[x2+. 2 x] is the interval [(5/4), 2], where [t] is the greatest integer ≤ t is

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Q. The sum of the maximum and minimum values of the function $f(x)=|5 x-7|+\left[x^2+\right.$ $2 x]$ is the interval $\left[\frac{5}{4}, 2\right]$, where $[t]$ is the greatest integer $\leq t$ is ______

JEE MainJEE Main 2022Complex Numbers and Quadratic Equations

Solution:

Graph of $x^2+2 x$
image
Graph of $| 5x - 7|$
image
$\left. f ( x )\right|_{\min }=4+0=4$, at $x=\frac{7}{5}$
$\left. f ( x )\right|_{\max }=8+3=11$, at $x =2$
Required sum $=15$