Find the domain of the function using interval notation

Question

G(x)=x+4/x³-4x

Answer 1

Shelley, I worry that you may have not given us the problem accurately. A lot of students make the mistake of not putting in parentheses around numerators and denominators.

If your original problem looked something like this:

X+4

G(x) = ———

X³ - 4x

then you needed to add parentheses when moving to simple text.

In particular, put parentheses around the numerator, and put a separate set around the denominator, as follows:

G(x) = (x+4) / (x³ - 4x)

Shelley, this Is a different function, and has a different answer.

First, simplify the denominator

G(x) = (x+4) / (x(x²-4))

= (x+4)/(x(x-2)(x+2))

Now the domain cannot include 0, 2, and -2, because those values would cause the denominator to become zero.

Answer 2

This must exclude x = 0; all other positive and negative numbers are included.

(-infinity,0) U (0,infinity).

You can write infinity with the horizontal figure-8.