Question

What is the domain and range of `f(x) =x^2/ (x^2-6)`?

Answer 1

Domain: `x≠sqrt6`

Range: `yinRR`

Explanation:

First, it is important to understand the distinction between domain and range.

Domain:
All possible `x`-values for the expression

Range:
All possible `y`-values for the expression

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Finding the Domain:

On the numerator, the `x`-value can be any real number

The denominator however, `≠ 0` since that would make the function undefined.

So, to find the number that `x` cannot equal in the function, we must write:

Denominator`=0`

`x^2-6=0`

`x^2=6`

`sqrt(x^2)=sqrt6`

`therefore x=sqrt6` when the function is undefined

This means that the domain is: `x≠sqrt6`

Finding the Range:

`f(x)` just means that `x` is the input of the function.

The actual result of the equation is `y`, do the function can be rewritten as:

`y=x^2/(x^2-6)`

Now there is a `y`-value to work with. Since there are no limitations on the value of `y` in the equation, it can be any real number.

This means that the range is: `yinRR`

or

`y` can be any real number