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

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:

(1) \(\left[\frac{1}{8}, \frac{1}{5}\right]\)

(2) \(\left[\frac{1}{7}, \frac{1}{6}\right]\)

(3) \(\left[\frac{1}{7}, \frac{1}{5}\right]\)

(4) \(\left[\frac{1}{8}, \frac{1}{6}\right]\)

Answer 1

Correct option is (4) \(\left[\frac{1}{8}, \frac{1}{6}\right]\)

\(\sin 5 \mathrm{x} \in[-1,1]\)

\(-\sin 5 \mathrm{x} \in[-1,1]\)

\(7-\sin 5 \mathrm{x} \in[6,8]\)

\(\frac{1}{7-\sin 5 x} \in\left[\frac{1}{8}, \frac{1}{6}\right]\)