Question

What is the domain and range of `f(x) = sqrt( x+3)`?

Answer 1

Domain: `x in [-3,+oo)`
Range: `f(x) in [0,+oo)`

Explanation:

Assuming we are limited to Real numbers:

The argument of the square root operation must be `>=0`
therefore
`color(white)("XXX")x+3 >= 0 rarr x >= -3`

The square root operation provides a (primary) value which is non-negative.
As `xrarr +oo, sqrt(x+3)rarr +oo`
So the range of `f(x)` is `0` to `+oo`