Functions
Range of a Function
JEE Main 2024
Grade 12
Question:
The range of $f(x) = \frac{1}{7 - \sin 5x}$ for $x \in \mathbb{R}$ is:
(1) $[\frac{1}{6}, \frac{1}{8}]$
(2) $[\frac{1}{8}, \frac{1}{6}]$
(3) $(\frac{1}{8}, \frac{1}{6})$
(4) $(0, \frac{1}{6})$
Step-by-Step Solution
Key Concept: $\sin 5x \in [-1, 1]$, so find the range of $7 - \sin 5x$, then take reciprocals — remember reciprocals reverse inequalities.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (2)