Q47 / 90 · JEE Main 2024 (06 Apr Shift 2) · Mathematics

Let $f(x)=\frac{1}{7-\sin 5 x}$ be a function defined on $\mathbf{R}$. Then the range of the function $f(x)$ is equal to ;

  • A
    $\left[\frac{1}{7}, \frac{1}{6}\right]$
  • B
    $\left[\frac{1}{8}, \frac{1}{5}\right]$
  • C
    $\left[\frac{1}{7}, \frac{1}{5}\right]$
  • Correct answer
    D
    $\left[\frac{1}{8}, \frac{1}{6}\right]$

Solution

$\begin{aligned} & \sin 5 x \in[-1,1] \\ & -\sin 5 x \in[-1,1] \\ & 7-\sin 5 x \in[6,8] \\ & \frac{1}{7-\sin 5 x} \in\left[\frac{1}{8}, \frac{1}{6}\right]\end{aligned}$

Hence, the correct answer is option: 'D'.

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