# JEE Corner (Mains +Advanced) # 2

Geometry Level 3

Let $$f: A \rightarrow B$$ and is given that $$f(x) =\log_2 \left (\sqrt{(\cos(\pi x) - \sin(\pi x) )(\cos(\pi x) + \sin(\pi x) ) - 1 } + 2 \right)$$ is real and $$g: A \rightarrow C$$ such that $$g(x) = \lfloor x \rfloor ^{\{ x \} }$$. Find the range of $$g(x)$$.

Note that $$\{x\}$$ denote the fractional part of $$x$$.

×