Notice that the function,Originally Posted by batman123
has a meaning for any . Now you want it in set notation, one way is to write implying that is any REAL number. Another way is to assign the interval . Meaning could be as small as you wish and as large as you wish. Now the range is the value, notice that is always a negative number thus, . Notice the square bracket indicating that can be equal to 0 which is true.
The function is defined for any thus we write (let me just remind you then infinity is not a number even I use it does not mean that it is). If you graph this line you will see the the value is anything thus we write .
The function is not defined for all it is undefined for thus, cannot be 0, thus we write (this might be tricky) - the circle bracket indicate which we are trying to state. If you graph this function, you will see the always has a value except for (because the equation has not solution). But besides for that always has a value thus we write, .
Let me give you a more challenging one,