Can someone please help me answer my last question? f(x)=(√(2x+8))/(x^(2)-2x ) To find the domain of the function in the interval notation

Question

Can someone please help me answer my last question?


`f(x)=(√(2x+8))/(x^(2)-2x )`

To find the domain of the function in the interval notation

Answer 1

Well we have a function and its body is a fraction so we need to handle those edge cases, namely division by 0.

That means solving the following equation,

`x^2-2x=0\implies x(x-2)\implies x_1=0,x_2=2`.

As we can see x must not be equal to 0 or 2 if we do not want to end up with division by zero situation.

The domain is therefore
`\mathbb{R}-\{0,2\}`.

Writing this as interval would be,

`x\in(-\infty,0)\cup(0,2)\cup(2,\infty)`.

Hope this helps.