find the domain of the function and express the answer in interval notation

Question

How do you solve this and express the answer in interval notation? Explain.

g(x) = 10/(x + 7)

Answer 1

For the function g(x) = 10/(x+7) the function is defined at all points where the denominator is not equal to zero. The only value that makes the denominator equal to zero is x = -7; this is a problem because we cannot divide by zero -- which makes our function undefined at this point. Therefore the function is defined for all real numbers except -7. Demonstrated in interval notation below.

(-∞,-7) U (-7,∞)