[Kimball]

Geo said:

"Question is find the domain and range of
f(x)=sqrt(x+4) (The square root of x+4)

The domain is [-4,infinty)
The correct answer for the range is [0,infinity)

My question is, why isn't the range all real numbers? (-infinity,infinity) In class the teacher worked the problem and he said plug in any domain value for x and see what you get for f(x) is never less then zero."

If you plug in a negative number less that -4, you end up with the square root of a negative number. This is not possible with real numbers, only imaginary, i.e. sqrt(-1) by defintion equals a funny little number called i (or sometimes j).

So:

sqrt(4) = +/- 2 and
sqrt(-4)=2i where 2i=sqrt(4*(-1))=sqrt(4)*sqrt(-1)=2*i

Complex math is, for the most part useless, except when you get into analyzing differential equations and AC electrical circuits. Believe it or not, that imaginary stuff is quite useful in the real world. Well, the real of world of us engineers and other math-type geeks.