Question #ff32b

1 Answer
Nov 19, 2017

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