How to modify a global variable within a function in bash?

I'm working with this:

GNU bash, version 4.1.2(1)-release (x86_64-redhat-linux-gnu)

I have a script like below:

#!/bin/bash

e=2

function test1() {
  e=4
  echo "hello"
}

test1 
echo "$e"

Which returns:

hello
4

But if I assign the result of the function to a variable, the global variable e is not modified:

#!/bin/bash

e=2

function test1() {
  e=4
  echo "hello"
}

ret=$(test1)

echo "$ret"
echo "$e"

Returns:

hello
2

I've heard of the use of eval in this case, so I did this in test1:

eval 'e=4'

But the same result.

Could you explain me why it is not modified? How could I save the echo of the test1 function in ret and modify the global variable too?

When you use a command substitution (i.e., the $(...) construct), you are creating a subshell. Subshells inherit variables from their parent shells, but this only works one way: A subshell cannot modify the environment of its parent shell.

Your variable e is set within a subshell, but not the parent shell. There are two ways to pass values from a subshell to its parent. First, you can output something to stdout, then capture it with a command substitution:

myfunc() {
    echo "Hello"
}

var="$(myfunc)"

echo "$var"

The above outputs:

Hello

For a numerical value in the range of 0 through 255, you can use return to pass the number as the exit status:

mysecondfunc() {
    echo "Hello"
    return 4
}

var="$(mysecondfunc)"
num_var=$?

echo "$var - num is $num_var"

This outputs:

Hello - num is 4