Final answer:
The function g(x) = 2 − sin(x) is not one-to-one because sine is a periodic function that repeats its range of values every 2π radians, meaning multiple values of x can produce the same g(x) value.
Step-by-step explanation:
The question asks whether the function g(x) = 2 − sin(x) is one-to-one. To determine if a function is one-to-one, every element of the range must be mapped from a unique element from the domain. In the case of the sine function, we know it is periodic and oscillates between +1 and -1. Because the sine function repeats its values every 2π radians, g(x) will not be a one-to-one function as there will be multiple values of x that will yield the same value of g(x), due to the periodic nature of the sine function.
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