SOLUTION: find the domain of function f(x) = root 2x - 3

There are two ways, graphically and algebraically.
I'll do the graphical way first.

First draw the graph of 

 

consider the x-axis as a number line, shade the part
that is directly underneath or above the curve. in 
this particular case the graph is entirely above the 
x-axis at and to the right of 1.5.  So shade the 
x-axis number line everywhere underneath the curve,
putting a darkened circle at the start of the shading,

 

And so the number line that represents the domain is
this number line:

 

which in interval notation is



and in set-builder notation is

   {x|x≧1.5}

To do it using only algebra:



No negative numbers can appear under square roots,
fourth roots, sixth roots, eighth roots or EVEN
roots in general.  (However negative numbers can
appear under cube roots, fifth roots, and odd roots
in general, but we only have an even root here.)

Therefore we must set what's under the square root
radical, which is  greater than or equal to 0:



and solve that for x



Divide through by 3:







You can write it any of the above three ways.

So we shade that on a number line:

-------------------@===================>
-3  -2  -1   0   1   2   3   4   5   6

That is the graph of the domain, which is the
same as the x-axis shaded under the graph above.

which in interval notation, as above, is



and in set-builder notation is

   {x|x≧1.5}

Edwin