Question

How do you find the domain of `f(x) = ((x + 8)^(1/2)) /( (x + 3)(x - 2))`?

Answer 1

`x in [-8;-3)uu(-3;2) uu (2;+oo)`

Explanation:

You can rewrite the given expression as:

`sqrt(x+8)/((x+3)(x-2)`

Then, since you cannot calculate the square root of a negative number and you cannot divide by zero, the domain is the solution of the following conditions:

`x+8>=0 and x+3!=0 and x-2!=0`

that's

`x>=-8 and x!=-3 and x!=2`

that can be written as:

`x in [-8;-3)uu(-3;2) uu (2;+oo)`