Question

The sum of the maximum and minimum values of the function |5x-7|+[x2+2x] is the interval $\left[\frac{5}{4}, 2\right]$, where $[t]$ is the greatest integer $\leq t$ is ______

Answer 1

The correct answer is 15
Graph of x2+2x

Graph of ∣5x−7∣

f(x)∣min​=4+0=4, at x=57​
f(x)∣max​=8+3=11, at x=2
Required sum =15