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JEE Main 20246 AprilEvening Shift
Exam
JEE Main
Year
2024
Date
6 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Functions

JEE Main 2024 · 6 April · Evening Shift · Mathematics · Functions

Let f(x)=(1)/(7- 5 x) be a function defined on R . Then the range...

Let f(x)=17−sin⁡5xf(x)=\frac{1}{7-\sin 5 x} be a function defined on R\mathbf{R}. Then the range of the function f(x)f(x) is equal to ;

Options

  1. A[17,16]\left[\frac{1}{7}, \frac{1}{6}\right]
  2. B[18,15]\left[\frac{1}{8}, \frac{1}{5}\right]
  3. C[17,15]\left[\frac{1}{7}, \frac{1}{5}\right]
  4. D[18,16]\left[\frac{1}{8}, \frac{1}{6}\right]

Correct answer

D. [18,16]\left[\frac{1}{8}, \frac{1}{6}\right]

Step-by-step solution

sin⁡5x∈[−1,1]−sin⁡5x∈[−1,1]7−sin⁡5x∈[6,8]17−sin⁡5x∈[18,16]\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}$$
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