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Basic question about functions

  1. May 15, 2009 #1

    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.


  2. jcsd
  3. May 15, 2009 #2


    User Avatar

    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" [Broken] such as 'plus or minus the square root', but they are not functions, strictly speaking. (they are relations)
    Last edited by a moderator: May 4, 2017
  4. May 15, 2009 #3
    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.
  5. May 16, 2009 #4
    Thanks guys. I always thought that the square root symbol always meant both +ve and -ve roots.

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