Question

How do you find the domain of `f(x)=(sqrt(x-9))/(x^2-16)`?

Answer 1

`{x|x≥9}` or `[9, oo[`

Explanation:

The domain is the set of numbers that `x` can be equal to.

Let's look at the numerator first. You can only take the square root of a number greater than or equal to `0`. That means that `x-9≥0` (else you will be taking the square root of a negative number). Solving this gives `x≥9`.

Let's then look at the denominator. You cannot divide by zero. This means that `x^2-16ne0`. Solving this gives `xne4vvxne-4`.

Combining these gives `x≥9 ^^ xne4 ^^ xne-4`. However, since `x≥9` implies that `xne-4` and `xne4`, we can remove both.

Our final answer is `x≥9`. In set notation, we write `{x|x≥9}`. In interval notation, we write `[9, oo[`.