Question

What is the domain of this function?

f(x)=(√(x+3))/((x+8)(x-2))

All real numbers except -8, -3, and 2

x ≥ 0

All real numbers

x ≥ -3, x ≠ 2

I was thinking that it could be either A or D, but i'm not sure.

Answer 1

Since it's a fraction, the denominator can't equal 0. So (x+8)(x-2) cannot equal 0. Also a square root can't be less than 0 because then you won't get a real number. So the square root of x+3 has to be greater than 0. Solve for (x+8)(x-2) = 0. And x would equal -8,2, and that means the domain can't be those two numbers. Next solve for \[x+3\ge0\]And you would get x is greater or less than -3. Since -8 is greater than -3, the domain would just be x ≥ -3, x ≠ 2. So it's C.

Answer 2

Wait, if you said that it cant be -8 or 2, why is it c?

Answer 3

C says \[x\neq2\]It means x is not equal to 2. The domain can't equal 2. So that's right. And since the domain has to be greater or equal to -3 (because of the square root), it already implies that the domain cannot be -8.

Answer 4

I see. Thanks!!! :)