Question

Explanation about domain of the function?

`f(x)=(3x-6)/(x^2-4)`

I dont understand why the numbers 2 and -2 are domain of the function

Answer 1

Domain: Every real number except `x=+-2`

`x inRR, x!=+-2`

Explanation:

The domain of a function is the set of all inputs for which the function is defined.

What makes a rational expression, like the one we have, undefined, is when the denominator is equal to zero.

Let's set the denominator of `f(x)`, `x^2-4` equal to zero.

Since we're dealing with a difference of squares, we can factor this as

`(x+2)(x-2)=0`

Setting both factors equal to zero, we get

`x=-2` and `x=2`

These are not in the domain of `f(x)`, because they will make the function undefined. If we plugged either one of those in, we would be dividing by zero.

The domain of `f(x)` is all `x`-values except `x=+-2`. We can write this with more mathy notation as

`x inRR | x!=+-2`

All this is saying is that the domain of our function includes every real number except for `x=+-2`.

Hope this helps!