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

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:\

Professor PC Thomas Classes · Answer

(c): Since, $-1 \leq \sin 	heta \leq 1 \forall 	heta$, so we have\ $-1 \leq \sin 5 x \leq 1$\ $\Rightarrow \quad-1 \leq-\sin 5 x \leq 1$\ $\Rightarrow \quad-1+7 \leq 7-\sin 5 x \leq 1+7$\ $\Rightarrow \frac{1}{8} \leq \frac{1}{7-\sin 5 x} \leq \frac{1}{6}$\ ⇒ Range $f(x)=\left[\frac{1}{8}, \frac{1}{6}ight]$\