f-x-cos-2pix-sin-2pix-x-x-find-R-f-

Question Number 185574 by mnjuly1970 last updated on 23/Jan/23

f (x) = c o s (2 π x) + s i n (2 π x) + \sqrt{⌊ x ⌋ + ⌊ - x ⌋}

f i n d R_{f} = ?

Commented by mahdipoor last updated on 23/Jan/23

\sqrt{[x] + [- x]} = {\begin{cases} 0 x \in Z \\ \sqrt{- 1} = i x \notin Z \end{cases}

\Rightarrow D_{f} = Z \Rightarrow f (x) = c o s (2 π k) + s i n (2 π k) + 0 = 1