# SAT1000 - P878

Algebra Level pending

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

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