Question

Finding the domain of the function in the interval notation
`f(x)=(√(2x+8))/(x^(2)-2x )`

Answer 1

The square root exists for
`2x+8\ge0\implies x\ge-4`, or on the interval
`[-4,\infty)`.

But
`f(x)` is undefined when its denominator is zero, which happens for

`x^2-2x=x(x-2)=0\implies x=0\text{ or }x=2`

so we need to remove these points from the interval above. Then the domain of
`f` is

`[-4,0)\cup(0,2)\cup(2,\infty)`