Final answer:
The domain of the function f(x) = (x² + 4)/(x - 2) is all real numbers except x = 2 because the denominator cannot be zero. Option c) x ≠ 2 correctly represents the domain.
Step-by-step explanation:
To find the domain of the function f(x) = (x² + 4)/(x - 2), we must look for values of x that would make the function undefined. The denominator of a fraction can never be zero because division by zero is undefined. Therefore, the only restriction on the domain of f(x) is that x cannot be equal to 2, as that would make the denominator zero. All other real numbers are acceptable values for x.
The correct domain of the function is "All real numbers except x = 2", which is sometimes written as x ≠ 2. Therefore, the choice that represents the domain is c) x ≠ 2.