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F(x)=2-e^-x/2
Domain and range

User Sybind
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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].

User Mike Ellis
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