If and , where denotes the greatest integer less than or equal to , then the range of…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

f(x)=\left\lfloor\frac{2x^2+2x+11}{x^2+x+4}\right\rfloor

and

g(x)=\log_2\left(\frac{x^2+1}{2x}\right)

, where

\lfloor x\rfloor

denotes the greatest integer less than or equal to

x

, then the range of

h(x)=\log_{g(x)}f(x)

is (a)

(-\infty,\infty)

(b)

(-\infty,\infty)\setminus\{0\}

(c)

[-1,\infty)

(d)

(-\infty,1]