Let f:mathbb Rtomathbb R be a function defined by f(x)=log_sqrt m \sqrt2(sin x-cos x)+m-2 \ , for some m , such that the range of f is [0,2] . Then the value of m is :

Functions: Let f:mathbb Rtomathbb R be a function defined by f(x)=log_sqrt m… | JEE Main 2023

JEE Main 2023 (Online) 25th January Evening ShiftQuestion 1

Let $f:\mathbb R\to\mathbb R$ be a function defined by $f(x)=\log_{\sqrt m}\left\{\sqrt2(\sin x-\cos x)+m-2\right\}$, for some $m$, such that the range of $f$ is $[0,2]$. Then the value of $m$ is :

Functions

$5$✓ Correct answer$3$$2$$4$

Solution

$\sqrt2(\sin x-\cos x)\in[-2,2]$, so the argument ranges over $[m-4,m]$. Range $[0,2]$ needs $m-4=1$ and $\log_{\sqrt m}m=2$; $m=5$.

Functions - JEE Mathematics question (JEE Main 2023 (Online) 25th January Evening Shift)

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