Final answer:
The set of preimages that maps onto 2 in the function f(x) = ⌈x⌉ is the interval (1, 2).
Step-by-step explanation:
The function f(x) = ⌈x⌉ maps real numbers to the closest integer. The symbol ⌈x⌉ represents the ceiling function, which rounds up to the nearest integer. In this case, f(x) maps every real number between two consecutive integers to the higher integer.
To find the set of preimages that maps onto 2, we need to find all x values for which ⌈x⌉ = 2. Since ⌈x⌉ is always an integer, the only possible values for x are between 1 and 2 (exclusive), since any real number between these values would round up to 2 when applied to the ceiling function.
Therefore, the set of preimages that maps onto 2 is the interval (1, 2). This means that any real number x in the interval (1, 2) would result in ⌈x⌉ = 2.