Final answer:
The domain of the function is all real numbers except x = 16, as it would make the denominator zero.
Step-by-step explanation:
The domain of a function is the set of all possible input values for which the function is defined. In this case, we have the function f(x) = (√x – 2) / (√x + 4).
To find the domain, we need to consider any restrictions on the input values. In this function, the denominator (√x + 4) cannot be zero since division by zero is undefined. So, we need to find the values of x that make (√x + 4) equal to zero.
Solving √x + 4 = 0, we get √x = -4. Squaring both sides, we get x = 16. Therefore, the domain of the function is all real numbers except x = 16, since it would make the denominator zero.