Question

What is the domain of y= 2x - 4/x^2 - 4?

Answer 1

`(-\infty,-2)\cup (-2,2)\cup (2,+\infty)`

Explanation:

The given rational expression is:

`y=(2x-4)/(x^2-4)`

We factor this expression to obtain:

`y=(2(x-2))/((x-2)(x+2))`

We can see that, this rational function has a hole at x=2 and a vertical asymptote at x=-2

Therefore the domain is

`x\\e 2\: and\:x\\e -2`

Or

`(-\infty,-2)\cup (-2,2)\cup (2,+\infty)`

Answer 2

{x while x ≠2, -2}

Explanation:

First let's define domain,

Domain is the set of all values on which the function is defined i.e. the function doesn't approach to infinity.

Given function is:

`y = (2x-4)/(x^(2) -4)`

We will look for all the values of x on which the function will become undefined:

We can see that x= 2 and x=-2 will make the denominator zero as there is x^2 involved. The denominator zero will make the function undefined.

So, the domain of the function is set of all real numbers except 2 nd -2 {x while x ≠2, -2} ..