Does the formula #f(x) = sqrt(x)# define a function ?

1 Answer
Aug 29, 2016

Yes #f# is a function. We do not have to restrict the codomain, but we can note that the range of #f# is #[0, oo)#

Explanation:

The expression #sqrt(x)# denotes the principal square root of #x#, which in the case of non-negative values of #x# is the non-negative one. The other, non-principal square root of #x# is then #-sqrt(x)#.

So the formula:

#f(x) = sqrt(x)#

defines a unique value for any non-negative value of #x#.

It thus defines a function.