Question

How do you find the domain and range of `f(x)= -sqrt(x-3)`?

Answer 1

Domain `{ x in RR, x>= 3}`
`{y inRR, y<= 0}`

Explanation:

For a function from real to real x-3 should be `>=0`, hence domain is `{ x in RR, x>= 3}`.

For range solve `y= -sqrt(x-3)` for x, and to note that y would have to be all negative real numbers.
`x= y^2 +3`, hence `y<=0` Range would be `{y inRR, y<= 0}`