Is the Square Root of a Number Always Considered a Function?

[pamparana]

Hello,

My calculus book is confusing and I am pretty sure this is an error. It describes a function as one where one distinct input will have one and only one distinct output. Fair enough.

The next example is output of f(x) = square root (x) when input is 25!

Clearly, this is not a function! This relation (obviously) does not result in a unique output for every unique input, right? square root (25) = +5 and -5.

Or am I missing something in function defs. The book does not even consider the negative value of a square root operation.

That's what I get for buying the idiot's guide...

Please let me know if I am missing something here.

Thanks,

Luca

 

[gel]

Your calculus book is correct. A function maps each element in the domain to a unique element in the range.
The square root function is usually defined to be the positive square root. Sometimes you can talk about http://en.wikipedia.org/wiki/Multivalued_function" such as 'plus or minus the square root', but they are not functions, strictly speaking. (they are relations)

 

[Pagan Harpoon]

This is why the +/- is needed next to the discriminant in the quadratic equation formula. If the square root symbol was understood to mean both positive and negative roots, it wouldn't be necessary.

 

[pamparana]

Thanks guys. I always thought that the square root symbol always meant both +ve and -ve roots.

cheers