SAT1000 - P878

Algebra Level pending

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

GIven that h(x)h(x) is the symmetric function of g(x)=4x2g(x)=\sqrt{4-x^2} respect to f(x)=3x+b (bR)f(x)=3x+b\ (b \in \mathbb R), h(x)>g(x)h(x)>g(x) is always true for all xx on the domain of g(x)g(x), then find the range of bb.

The range can be expressed as (L,+)(L,+\infty), submit L2L^2.

Have a look at my problem set: SAT 1000 problems


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