Expert: Sherry Wallin - 7/26/2009

Question
QUESTION: Hi there;
I'm confused how to do this with a sqrt.  Can you walk me thru this please?

f(x) = radical 4 sqrt(x^2=2x)

Does this make sense?


ANSWER: Hi Susan~
    
What do you mean by radical 4 sqrt? Are you trying to say the 4th root? Also you have x^2 = 2x is that suppose to be +?

Math Prof

---------- FOLLOW-UP ----------

QUESTION: Yes!  Sorry about that.  See it's been a VERY long time :)  

4th root x^2+2x

Thank you!

Answer
Susan~
    Any even root has to have the value under the radical greater than or equal to 0, i.e., the value under the radical can't be negative. So really all you have to do is examine where x^2 + 2x is greater than or equal to 0: x^2+2x >= 0 factor
which says that x(x+2)>= 0, set x(x+2) equal to 0 which says x => 0 or x + 2 >= 0 which says that x>= 0 or x >= -2. Now  put your values on a number line:
<------------------------->
         -2          0   
Divide the number line into 3 pieces:(-00, -2], [-2,0], and [0, 00). Choose a value in each of those intervals, (I will use -3 in (-00,-2], -1 in [-2,0],and 1 in [0, 00). -3,-1, 1  are called test values and -2 and 0 are called critical values. Remember you are testing where x^2+2x = x(x+2)>= 0 so plug the test values in: -3(-3+2)= -3(-1) = 3 and 3>=0 so the interval (-00, -2] is part of the domain. Check the next test value: -1(-1+2)= -1(1)= -1 which is not greater than or equal to 0 so you have to exclude the interval [-2,0]. And finally check 1: 1(1+2) = 1(3) = 3 >= 0 so the interval [0,00) is part of our domain. To sum this up then the domain is (-00,-2] union [0,00). I hope this is clear.

Math Prof

Note 00 is infinity and -00 is negative infinity