Question

How do you find the domain of `f(x)=-x^2-5x+6`?

Answer 1

It's a polynomial function, so the domain is all real numbers, `RR`.

Explanation:

Since this equation is a polynomial function (quadratic functions are polynomial) its domain includes all real numbers, `RR`.

In general, to find the domain of a function you would have to find which values of `x` are restricted, meaning they would give an indefinite `y` or `f(x)`.

A restricted `x` value would usually arise in a case such as:
`f(x) = (3x^2 + 2)/(x-1)`
where an `x` value of 1 would give a denominator of 0, yielding an indefinite value for `f(x)`. Then, `x=1` is a restricted value.

But in this case, any real value of `x` will give a real value of `f(x)`, so the domain includes all real numbers.