Question

Question #ff32b

Answer 1

The Domain of a function, f(x), is all of the allowable x-values.

Explanation:

If I read your function correctly, it's:

`y = x - (4/x^2) - 2x - 15`.

If this is correct, then let's first combine the `x` and the `-2x`,

which gives us: `x - 2x = -x`.

So the function is: `y=(4/x^2) - x - 15`.

This is a polynomial with the `x^2` term in the denominator.

If the `x^2` term were not in the denom., the domain would be All Reals: `(-oo,oo)`.

But the `x^2` term IS in the denominator, so we have to limit the domain to All Real numbers except zero, since division by zero is undefined.

So, the Domain is: `(-oo, 0) uu (0, oo)` -- the Union of these two sets, from negative infinity up to but not including zero, and from (but not including) zero to positive infinity.

We can plug in a negative or positive real number for `x`, but not zero.

You know that square brackets -- [ ] -- mean that the endpoint of the interval is included, and that round brackets (parentheses) mean that the endpoint of an interval is not included, right?

Connie