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 $m$, such that the range of $f$ is $[0,2]$. Then the value of $m$ is $............$
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 $m$, such that the range of $f$ is $[0,2]$. Then the value of $m$ is $............$
- [JEE MAIN 2023]
- A
$5$
- B
$3$
- C
$2$
- D
$4$
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- [KVPY 2013]