Question

For real values of x, range of the function $y = \frac{1}{2 - \sin 3x}$ is

• A. $\frac{1}{3} \leq y \leq 1$
• B. $- \frac{1}{3} \leq y < 1$
• C. $- \frac{1}{3} > y > - 1$
• D. $\frac{1}{3} > y > 1$

Answer 1

Answer: (A)

$\frac{1}{3} \leq y \leq 1$

Answer 2

$\because y = \frac{1}{2 - \sin 3x}$, $\therefore 2 - \sin 3x = \frac{1}{y}$ $\Rightarrow \sin 3x = 2 - \frac{1}{y}$

Now since,

$$$\Rightarrow 1 \leq \frac{1}{y} \leq 3 \Rightarrow \frac{1}{3} \leq y \leq 1$.