Final answer:
Functions f(x)= 4-x and f(x)= 1-x³ are one-to-one, while a function represented as f(x)= 2 is not one-to-one.
Step-by-step explanation:
To determine if the functions are one-to-one, we must check if each input corresponds to one unique output and vice versa. The first function, f(x)= 4-x, is clearly one-to-one because it's a linear function with a non-zero slope. This means for every x-value, there's only one y-value. So, it passes the Horizontal Line Test, indicating one-to-one behavior.
The second function is not explicitly given, but if we assume it's f(x)= 2, it would not be one-to-one since it's a horizontal line, meaning multiple inputs (x-values) correspond to the same output (y-value 2).
For the third function, f(x)= 1-x³, since the exponent is odd, it represents an odd function. Odd functions are always one-to-one since they are symmetric about the origin and pass the Horizontal Line Test. Hence, f(x) is one-to-one on the real number set (R).