Question

The range of the function y = `1/(2 - sin3x)` is ______.

विकल्प

• `(1/3, 1)`

• `[1/3, 1)`

• `[1/3, 1]`

• `(1/3, 1]`

Answer 1

The range of the function y = `1/(2 - sin3x)` is `underlinebb([1/3, 1].`

Explanation:

y = `1/(2 - sin3x)`

–1 ≤ sinθ ≤ 1

–1 ≤ sin3x ≤ 1

1 ≥ –sin3x ≥ –1

3 ≥ 2 – sin3x ≥ 1

`1/3  ≤ 1/(2 - sin3x) ≤ 1`

∴ Range = `[1/3, 1]`