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

Dec 27, 2016

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:

$x + 8 \ge 0 \mathmr{and} x + 3 \ne 0 \mathmr{and} x - 2 \ne 0$

that's

$x \ge - 8 \mathmr{and} x \ne - 3 \mathmr{and} x \ne 2$

that can be written as:

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