The domain of the function f(x) = 2 - e^(-x/2) is all real numbers, and the range of the function is from negative infinity to 2, inclusive.
The function given is f(x) = 2 - e-x/2. To find the domain of this function, consider the types of numbers that you can substitute for x without causing any mathematical issues. Since there is an exponential function involved and exponential functions are defined for all real numbers, the domain of f(x) is all real numbers, or (−∞, ∞).
The range of the function refers to the possible values of f(x). As x approaches infinity, e-x/2 approaches zero, making f(x) approach 2. As x approaches negative infinity, e-x/2 grows without bound, but since it is subtracted from 2, the function approaches negative infinity. Therefore, the range is (−∞, 2].