# 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 \(x\).