Question

How do you find the domain and range of `sqrt(1-sinx)`?

Answer 1

With a radical expression we have to make sure the argument is never negative.

Explanation:

Whatever value `x` takes `sinx` will be between `-1and+1`
So the argument (`1-sinx`) will between `0and+2`
Conclusion: the domain is unlimited `(-oo,+oo)`

The range falls between `sqrt0and sqrt2` inclusive (see above)
Or `[0,sqrt2]`