Find the domain. f(x)=√9-x^2/x-1

Answer 1

First, note my assumption---without the parentheses, the expression is ambiguous

f(x)=√9 - x^2 / (x - 1)

It is also possible that you meant:

f(x) = (√9 - x^2) / (x - 1)

Let's do this one first.......

First, if x = 1, the expression becomes undefined.

For large x, simplify to get:

-x^2 / x = -x

For large -x:

-x^2 / -x = +x

So: the domain is simply: x < 1 < x, or simply x ≠ 1

If it is this one:

f(x)=√9 - x^2 / (x - 1)

We have the same behavior at x = 1

For large values of x, this is the same as the 1st case. At lower values of x, the curves are different, but the domain is the same