Find the domain of the function
g(x)= 3x/x^2 -49
I try to figure it out it, and since x^2-7 is a perfect square (x+7)(x-7), I thought x couldn't be +-7?
To find the domain of a function, we need to identify any values of x that would result in an undefined expression. In this case, the expression in the denominator is x^2 - 49.
You correctly noted that x^2 - 49 can be factored as (x + 7)(x - 7). Thus, we know that the expression in the denominator will be equal to zero when x = -7 or x = 7. At these points, the function is undefined because division by zero is not defined in mathematics.
Therefore, the domain of the function g(x) = 3x/(x^2 - 49) is all real numbers except x = -7 and x = 7. Symbolically, we can express the domain as:
(-∞, -7) ∪ (-7, 7) ∪ (7, ∞)
So, all real numbers except -7 and 7 are included in the domain of the function.