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

Question

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

Accepted Answer

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

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