In algebra what does: "Is defined for" mean?
I have a question posted:
$\sqrt{a+b}$ is defined for $-b \leq a$.
The question posed is: Is this true…
My question: WHAT DOES "Is Defined For" mean??
[Math] Algebra: What does “is defined for” mean
algebra-precalculusterminology
Best Answer
If $\sqrt{a+b}$ is said to be defined for ${-b}\leq{a}$, then $\sqrt{a+b}$ is not necessarily defined for ${a}<{-b}$.
The reason for this, is that if ${a}<{b}$, then $\sqrt{a+b}$ could be the square root of a negative number, which is undefined (at least, when restricted to Real numbers).
So simply put, if a function is said to be defined for a certain range, then that means the function will provide a value for that range. And if the range is not satisfied, the function will quite possibly be undefined (that is, the function does not give a legitimate value), though without any further information we cannot be sure.
So if you're answering a question and you're given an expression and the range for which it is defined, you can only use said equation if the defined ranged is satisfied, as the expression may not be true for other values outside the range.