QJEEM24Ma8455: JEE Main 2024 Mathematics - Class 11 JEEM24Ma8455 Solution: Let f ( x ) = 1 7 − sin ⁡ 5 x be a function defined on R . Then …

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QJEEM24Ma8455: JEE Main 2024 Mathematics - Class 11 JEEM24Ma8455 Solution: Let f ( x ) = 1 7 − sin ⁡ 5 x be a function defined on R . Then …

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

Multiple Choice Options

A [18,15]
B [17,16]
C [17,15]
D [18,16]

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Accepted Answer

$\begin{aligned} f (x) = \frac{1}{7 - \sin 5 x} \\ - 1 \leq \sin 5 x \leq 1 \\ - 1 \leq - \sin 5 x \leq 1 \\ - 1 + 7 \leq 7 - \sin 5 x \leq 1 + 7 \\ 6 \leq 7 - \sin 5 x \leq 8 \\ \frac{1}{8} \leq \frac{1}{7 - \sin 5 x} \leq \frac{1}{6} \\ \frac{1}{8} \leq f (x) \leq \frac{1}{6} \\ Range = [\frac{1}{8}, \frac{1}{6}] \end{aligned}$

QJEEM24Ma8455: JEE Main 2024 Mathematics - Class 11 JEEM24Ma8455 Solution: Let f ( x ) = 1 7 − sin ⁡ 5 x be a function defined on R . Then …

Multiple Choice Options

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