Question

find the domain of the function algebraically and write it using interval notation: g(x) = 1/x + 8/(x+5)

Answer 1

When a domain exists, that means that when you put in a x-value, the outcome is not does not exist. There are a couple of cases when this is true:
When you divide by zero
Take the square root of a negative number.
There are no square roots in the function, so we have to be worried if there is something being divided by x.

Answer 2

So, you get each denominator, and set each of them to zero, to see when you divide by zero. Set "x" to zero and "x+5" to zero, and those answers you find are the domain restrictions; everything else except those x-values (the ones you found), are in the domain. Need more help?

Answer 3

so what is the answer in interval notation?

Answer 4

I looked it up, what interval notation was, and I think it is like that;