Question

How do you find the minimum value of a square root function `f(x)= 3-sqrt(x+2)`?

Answer 1

This one has no minimum value.

As `x` gets larger, the root gets larger, and the function as a whole becomes more and more negative (slowly but certainly).

Or, in "the language": `lim_(x->oo) f(x)=-oo`

It does have a maximum though:
The expression under the root may not be negative, it may be `0`. This happens when `x=-2->f(x)=3`
graph{3-sqrt(x+2) [-3.85, 47.45, -12.5, 13.2]}

Domain: `x>=-2`
Range: `f(x)<=3`