Let f ( x ) = 1 7 - sin 5 x be a function defined on R. Then the range of the function f ( x ) is equal to : [2024]

Question

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 : [2024]

Smart Achievers · Accepted Answer

(3)

Since, $- 1 \leq sinθ \leq 1$ $\forall θ$ , so we have

$- 1 \leq \sin$ $5 x \leq 1$

$\Rightarrow - 1 \leq - \sin 5 x \leq 1$

$\Rightarrow - 1 + 7 \leq 7 - \sin 5 x \leq 1 + 7$

$\Rightarrow \frac{1}{8} \leq \frac{1}{7 - \sin 5 x} \leq \frac{1}{6}$

$\Rightarrow Range f (x) = [\frac{1}{8}, \frac{1}{6}]$

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