Find the range of the function .
Find the range of the function $f(x) = \frac{1}{3 - 2\sin x}$.
Answer
Answer
AIWritten by AI (gemini-2.5-pro) - it can contain mistakes.
For all $x \in \mathbb{R}$, $-1 \le \sin x \le 1$.
Multiplying by $-2$: $-2 \le -2\sin x \le 2$.
Adding 3: $1 \le 3 - 2\sin x \le 5$.
Taking reciprocals:
$\frac{1}{5} \le \frac{1}{3 - 2\sin x} \le 1$.
Therefore, the range of $f(x)$ is $\left[\frac{1}{5}, 1\right]$.
From ISC 2026 Mathematics Paper 1, question 3(ii).