Find the domain and range of the function `f(x)=1/(2-sin3x)` .

Explanation

`f(x) = 1/(2-sin3x)`

Here, `2-sin3x` can never be zero as `sin3x` will always less than `2`.

`:.` Domain of `f(x)` will be `x in R.`

Now, `f(x)` will be maximum when `2-sin3x` is minimum.

`2-sin3x` will be minimum when `sin3x = 1.`

`:. f(x)_max = 1/(2-1) = 1`

`f(x)` will be minimum when `2-sin3x` is maximum.

`2-sin3x` will be maximum when `sin3x = -1`.

...