GATE 2023 IN – Question 57
For $g(x)=\max\{(x-2)^2,-2x+7\}$ on $\mathbb R$, the minimum value is ______ (one decimal place).
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Correct answer: 0.9 to 1.1
Explanation
The curves intersect where $(x-2)^2=-2x+7$, giving x = −1, 3. For $x\le3$, the line is at least 1; for $x\ge3$, the parabola is at least 1. At x = 3 both equal 1.
Thus the global minimum is **1.0**.