Question
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 _________
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 _________