Domain of a Function: Real vs Complex Numbers

[davon806]

Homework Statement

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?

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

If your textbook 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.

 

[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.

 

[symbolipoint]

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

 

[davon806]

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

 

[Mark44]

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.