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

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