The domain of a function is the set of all possible input values (x) for which the function is defined.
The range of a function is the set of all possible output values (f(x)) that the function can produce.
For the given function f(x) = 2^(x+1), the domain includes all real numbers because we can substitute any real number for x and obtain a valid output.
To find the range, we can examine the behavior of the function as x approaches positive and negative infinity. As x approaches negative infinity, the exponent (x+1) becomes very large negative number, and 2^(x+1) approaches zero. As x approaches positive infinity, the exponent (x+1) becomes very large positive number, and 2^(x+1) approaches infinity. Therefore, the range of the function is (0, infinity).
So, the domain is (-infinity, infinity) and the range is (0, infinity).