Domain of a fractional radical

Text

Find the natural domain of $f(x)=\dfrac{\sqrt{x+4}}{x-2}$.

Solution

Two conditions are required:

• the radicand must be non-negative: $x+4\ge 0\Rightarrow x\ge -4$;
• the denominator must be non-zero: $x-2\ne 0\Rightarrow x\ne 2$.

Intersecting the two conditions: $\boxed{\,D=[-4,\,2)\cup(2,\,+\infty)\,}$