The domain and range of the function $f(x)=\log_2\frac{\sin x-\cos x+3\sqrt{2}}{\sqrt{2}}$ are given by
Answer & explanation
Correct answer: option 1
$\frac{\sin x+\cos x}{\sqrt{2}}+3=\sin(x-π/4)+3$
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]