The domain and range of the function $f(x)=\log_2\frac{\sin x-\cos x+3\sqrt{2}}{\sqrt{2}}$ are given by

$D_f=(-∞,∞),R_f=[1,2]$ $D_f=(-∞,0)∪(0,∞),R_f=[-1,1]$ $D_f=(0,∞),R_f=[1,2]$ none of these

$D_f=(-∞,∞),R_f=[1,2]$

$\frac{\sin x+\cos x}{\sqrt{2}}+3=\sin(x-π/4)+3$ so $-1≤\sin(x-π/4)≤1$ $⇒2≤(\sin(x-π/4)+3)≤4$  $⇒x ∈ R=(-∞,∞)$ = Domain $1≤\log_2(\sin(x-π/4)+3)≤2$ ⇒ Range = [1, 2]