Functions

Let \(f:\mathbb{R}\to\mathbb{R}\) 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 _________