SAT1000 - P878

Given the function $y=f(x)\ (x \in \mathbb R)$ , for function $y=g(x)\ (x \in I)$ , let's define symmetric function of $g(x)$ respect to $f(x)$ as $y=h(x)\ (x \in I)$ , $y=h(x)$ is such that $\forall x \in I$ , point $(x,h(x)), (x,g(x))$ are symmetric about point $(x,f(x))$ .

GIven that $h(x)$ is the symmetric function of $g(x)=\sqrt{4-x^2}$ respect to $f(x)=3x+b\ (b \in \mathbb R)$ , $h(x)>g(x)$ is always true for all $x$ on the domain of $g(x)$ , then find the range of $b$ .

The range can be expressed as $(L,+\infty)$ , submit $L^2$ .

Have a look at my problem set: SAT 1000 problems