Let f (x)=
x + 32
− 4
x − 13
Choose the correct interval form for the DOMAIN of f and then enter the values for the endpoint(s) in the appropriate answer blank(s). Enter N/A in any unused blanks.
To determine the domain of a function, we need to identify the values of x for which the function is defined. In this case, we have a rational function with two expressions in the numerator and denominator:
f(x) = (x + 32) - 4 / (x - 13)
To find the domain, we need to consider two things:
1. We cannot divide by zero. So, the denominator (x - 13) cannot be equal to zero. Solving for x gives us x ≠ 13.
2. There are no other restrictions on the variable x. Since there are no square roots, logarithms, or any other operations that might result in undefined values, we can conclude that all other real numbers are valid.
Therefore, the domain of f(x) is all real numbers except x = 13. We can represent this interval form as (-∞, 13) U (13, ∞), where (-∞, 13) represents all real numbers less than 13, and (13, ∞) represents all real numbers greater than 13.
The value 13 is the only endpoint for this domain. So, the correct interval form and the value for the endpoint(s) are:
(-∞, 13) U (13, ∞) (13)