Determine the domain for the function. f(x)= square root x+3 over (x+8)(x-2)

Question

 please help me asap :)

Answer 1

Well, what's under the radical can't be negative, so...

 

x + 3 ≥ 0

x ≥ -3

 

The denominator can't be 0, so neither factor can equal 0.

 

x + 8 = 0

x = -8

 

x - 2 = 0

x = 2

 

Since -8 is already not ≥ 0, we can leave that out.

 

x ≥ -3

x ≠ 2