Math Is Fun Forum

Daniel123

Member

Registered: 2007-05-23

Posts: 663

Functions

Just a quick question.

For the function f(x) = x² + 5, state the range.

I put f(x) ∈ R, f(x) ≥ 5.

The book says that f(x) ≥ 5, x ∈ R.

I wouldn't have thought you had to restrict the domain... doesn't f(x) ≥ 5 imply that x ∈R?

Thanks.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Functions

No, it doesn't.  Functions can go from any set to any set.  For example, here is the standard metric on the complex numbers:

As you can see with this function, d(z) is in R, but this does not mean that z is in R.  Now of course, it all depends on how the function is defined.  It looks like the definition of your function is:

If that is the case, saying that x is in R is redundant.  x is in R by definition.  Then again, so is f(x).

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."