Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function defined by \(f(x)=\log _{\sqrt{m}}\{\sqrt{2}(\sin x-\cos x)+m…

Let \(f: \mathbb{R} \rightarrow \mathbb{R}\) be a function defined by \(f(x)=\log _{\sqrt{m}}\{\sqrt{2}(\sin x-\cos x)+m-2\}\), for some \(m\), such that the range of \(f\) is \([0,2]\). Then the value of \(m\) is

[JEE Main 2023, 25 Jan (Shift 2)]