GATE IN 2023 | Question: 47

Question

Consider the real-valued function $g(x)=\max \left\{(x-2)^2,-2 x+7\right\}$, where $x \in(-\infty, \infty)$. The minimum value attained by $g(x)$ is_____________(rounded off to one decimal place).

Answer 1

Ans : 1.0

g(x)=max⁡{u(x),v(x)}, the minimum of g typically occurs at a point where the two functions cross (so their values are equal) provided that at that crossing the common value is as small as possible.