IIT JAM 2023 Question 2: Concavity, convexity and quasi-concavity

Let $f, g : \mathbb{R} \to \mathbb{R}$ be $f(x)=x+2$ for $x\le1$, $2x+1$ for $x>1$; and $g(x)=2x$ for $x\le2$, $x+2$ for $x>2$. Then