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Mathematics · Functions

JEE Main 2024 — 6 April, Shift 2 — Question 16

Let f(x)=17−sin⁡5xf(x)=\frac{1}{7-\sin 5 x} be a function defined on RR.

Then the range of the function f(x)f(x) is equal to:

  1. Option A:

    [18,15]\left[\frac{1}{8}, \frac{1}{5}\right]

  2. Option B:

    [17,16]\left[\frac{1}{7}, \frac{1}{6}\right]

  3. Option C:

    [17,15]\left[\frac{1}{7}, \frac{1}{5}\right]

  4. Option D:

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

    Correct

Answer: D

Step-by-step solution

sin⁡5x∈[−1,1]\sin 5 \mathrm{x} \in[-1,1]

−sin⁡5x∈[−1,1]-\sin 5 x \in[-1,1]

7−sin⁡5x∈[6,8]7-\sin 5 x \in[6,8]

17−sin⁡5x∈[18,16]\frac{1}{7-\sin 5 x} \in\left[\frac{1}{8}, \frac{1}{6}\right]

Answer key and solution verified before publishing.

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Exam
JEE Main 2024
Paper
6 April, Shift 2
Subject
Mathematics
Chapter
Functions
Topic
Domain & range of functions
Let f(x)=1/7-sin 5 x be a function defined on R . Then the range of… | JEE Main 2024 PYQ with Solution · DhiX AI