Final answer:
The domain of the function F(x) = 5/(x-2) is all real numbers except 2, and the range is all real numbers, as the function value can approach any real number given different inputs for x, disregarding the asymptote at x=2.
Step-by-step explanation:
The domain and range of the function F(x) = 5/(x-2) are sets of all possible x and y values for which the function is defined and takes on values, respectively. For the domain, x can be any real number except the value that makes the denominator zero. In this case, x cannot be equal to 2, because 2 - 2 would result in division by zero, which is undefined. Therefore, the domain of F(x) is all real numbers, x ∈ R, x ≠ 2.
The range of F(x) is all real numbers because as x approaches infinity or negative infinity, the values of F(x) approach zero, and as x approaches 2 from the right or left, the function approaches negative or positive infinity, respectively. Hence, the range is all real numbers, y ∈ R.