Expert: Paul Klarreich - 10/5/2007

Question
How do you find the domain of a function with a square root in it for example    f(x)= sqr x(x-1)
I also have to find the limit.  so could you help me find the limit too.

thanks


Answer
Questioner:   Veronica
Category:  Calculus
Private:  No
 
Subject:  Calculus problem
Question:  How do you find the domain of a function with a square root in it, for example    f(x)= sqr x(x-1)
I also have to find the limit.  so could you help me find the limit too.

thanks
..............................................
Hi, Veronica,

If a function contains a square root, then the radicand (expression inside the radical symbol) must be nonnegative.  

Mathematicians write "nonnegative" as  ">= 0"

Now your function:

f(x)= sqr x(x-1)

is not totally clear.  As written, it means:

f(x) = sqrt(x) TIMES (x-1)

and the radicand is  x.  In that case, the domain requires that  x >= 0.

But if you meant (and you must write it this way)

f(x)= sqr(x(x-1))

Now the radicand is   x(x - 1), so you write the inequality:

x(x - 1) >= 0

That's more complicated.  You have two parts:

x >= 0  and  x >= 1,  which means  x >= 1

AND A SECOND PART:

x <= 0  and  x <= 1, which means  x <= 0

So the domain will be all x  EXCEPT  0 < x < 1

..............................

For a limit, you need a value of x to approach, but this function will be continuous for all x in its domain, so you will be able to substitute.