Question: Activity 20 - Properties of Functions 6. If function f is onto, a. Ca n the domain have more elements than the codomain? b. C

Activity 20 - Properties of Functions 6. If function f is onto, a. Ca n the domain have more elements than the codomain? b. C an the codomain have more elements than the domain? 7. If function f is one-to-one, c. Can the domain have more elements than the codomain? d. Can the codomain have more elements than the domain? 8. If function f is invertible, e. Can the domain have more elements than the codomain? f. Can the codomain have more elements than the domain? THEOREM Z Let f:A >B be a function, where A and B are finite sets of sizes m and n, respectively If f is one-to-one then msn . If f is onto, then m2n . If f is invertible, then m n Application: For each of the following functions, decide if it is one-to-one, onto, invertible or none of these 1. a. f: Q-Q with rule f(x) 3x+ 1 b. f QQ+ with rule fix)- 7x+ 5 c. : N- N with rule f(x) is the closest value for x

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