Question

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

Answer 1

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.