# Homework Help: Domain of a function

1. Nov 18, 2012

### davon806

1. The problem statement, all variables and given/known data
Consider some simple single-variable function such as
f(x)=2x+1
The domain,codomain and range of the above function is set of all real numbers.
But why not the set of all complex numbers?
if x = 3+4i
f(x) = 6+8i + 1 = 7+8i,so it is possible for x to be a complex no?

2. Relevant equations

3. The attempt at a solution

2. Nov 18, 2012

### HallsofIvy

If your text book has not dealt with complex numbers, then the "default" number system is the set of real numbers. It really should be stated somewhere in your textbook, perhaps in the preface of first chapter, but not necessary with each problem.

3. Nov 19, 2012

### davon806

My book has mentioned complex no before,but the author still wrote down the domain is the set of all real numbers instead of complex numbers.

#### Attached Files:

• ###### IMG_5422.JPG
File size:
118.9 KB
Views:
105
4. Nov 19, 2012

### symbolipoint

The range and domain are complex numbers a+bi for which b=0. Your function uses only Real Numbers.

5. Nov 19, 2012

### davon806

That means the range and domain of this function are the set of complex number?

6. Nov 19, 2012

### Staff: Mentor

You attached an image of the problem solutions. How is the problem presented? There might be a clue that the author intended the domain to be the reals.