what is the domain of the function in interval notation? g(x)=x+9/x^2-25

Answer 1

To find the domain of a function, we must just find the values of x that cannot be used. In this case, we know that the denominator of a fraction cannot be 0 since it will lead to an undefined answer. We can set the denominator equal to zero like so to find the values of x that are excluded from the domain:

x² - 25 = 0

x² = 25

x = 5, -5

We can then conclude that x can be equal to all numbers except 5 and -5. Written in interval notation, that looks like this:

(-∞, -5)U(-5, 5)U(5, ∞)