# f:X to Yf(x)=sinx+cox+2root2 is invertible then X to Y is

$\\f(x)=\sqrt2 *sin(x+{ \pi \over 4})+2\sqrt2 \\or f(x)=\sqrt2 *cos(x+{ \pi \over 4})+2\sqrt2 \\=>Y=[\sqrt2,3\sqrt2] \\=>X=[{-3\pi \over 4},{ \pi \over 4}] or [{\pi \over 4},{ 5\pi \over 4}]$