Let [f(x)=(1)/(7- 5 x)] be a function defined on [R].

Question

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

Accepted Answer

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

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