The range of the function ` f(x) = (1)/(2-sin 3x)` isA. `(1//3, 1 )`B. `[1//3, 1 )`C. `[1//3, 1]`D. none of these

The range of the function ` f(x) = (1)/(2-sin 3x)` isA. `(1//3, 1 )`B.

1.	The range of the function ` f(x) = (1)/(2-sin 3x)` isA. `(1//3, 1 )`B. `[1//3, 1 )`C. `[1//3, 1]`D. none of these
Answer» Correct Answer - C Cleary, domain of `f(x)` is R and `f(x) lt 0` for all `x in R` Let `y = f(x)`. Them `y = (1)/(2-sin 3x)` `rArr sin 3x = (2y-1)/(y) rArr x = (1)/(3) sin^(-1)((2y-1)/(y))` For x to be real, we must have `rArr -1 le (2y-1)/(y) le 1` `rArr - y le 2y -1 le y" "[beacuse y = f(x) gt 0]` ` rArr -y le 2y - 1 and 2y - 1 le y` `rArr y gt (1)/(3) and y le 1 rArr y in [1//3,1]` Hence, range `(f) = [1//3,1]`

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