10. Prove if the following functions are one-to-one or not. a. f:R-R, f(x) = x³ b. f: R-R, f(x) = x² + 1 11. Suppose tha

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10 Prove If The Following Functions Are One To One Or Not A F R R F X X B F R R F X X 1 11 Suppose Tha 1 (45.86 KiB) Viewed 65 times

10. Prove if the following functions are one-to-one or not. a. f:R-R, f(x) = x³ b. f: R-R, f(x) = x² + 1 11. Suppose that f: (1,0)³ (1,033, and we define f as taking the first 1 in the string and transforms it into a 0 an takes the first 0 in the string and transforms it into a 1. If the function has no zeros initially, then no zeros will be changed. If the function has no ones initially, then no ones will be changed. For example, 000 would become 001. Prove or give a counterexample if f is one-to-one, onto and/or a bijection. 12. Suppose that you wanted to construct a function that mapped one of the 50 states in the U.S. onto the 100 Senators of the United States. Explain if such a function can be constructed. Make sure that in your explanation you include the following vocabulary: well-defined function, onto, domain and range. 13. Give examples of the following from (1,0)m(1,0)m, you can choose what m is, but it must be the same in both the domain and the range. a. One-to-one, but not onto b. Onto, but not one-to-one c. A bijection. This function cannot be the identity function.