find the domain of the function:
f(x)=sqrt(4-x^2)/sqrt(1-x^2)

Question

find the domain of the function:
f(x)=sqrt(4-x^2)/sqrt(1-x^2)

barrycarter · Answer

Hint: you can't take the square root of a negative number

anonymous · Answer

would i set the top and bottom equation > 0?

barrycarter · Answer

The top one greater than or equal to 0, the bottom one greater than 0 (since you can't divide by 0)

anonymous · Answer

i did that and for the top i got x less than or equal to pos./neg. 2 and the bottom x< pos/neg 1

barrycarter · Answer

OK, and since BOTH those conditions must be true, x must be between -1 and 1

anonymous · Answer

i got the right answer but im just confused why the pos./neg. 2 isn't on there

barrycarter · Answer

Oh, because if x is between -1 and 1, it's already between -2 and 2.

anonymous · Answer

im still a bit confused why you cant use -2 and 2 as the answer lol

barrycarter · Answer

Oh, because both conditions have to met. In other words x has to be between -2 and 2 AND also between -1 and 1.

anonymous · Answer

oh alright i think i get that. i mite need more practice to make sure tho. thanks!

barrycarter · Answer

OK, try with a number like x=1.5 which is between -2 and 2, but not between -1 and 1. Does it work?

anonymous · Answer

why did you pick that number tho? how would i know what number to pick as x

barrycarter · Answer

Well, you said -2 < x < 2 might be the answer. I'm just pointing out that's not the case by choosing a number between -2 and 2 that doesn't work.

anonymous · Answer

oh okay i think i get what you're saying now!