Problem 46E

Indicate which of the functions in the referenced exercise are one-to-one correspondences. For each function that is a one-to-one correspondence, find the inverse function.

Exercise

a. Define g: Z → Z by the rule g(n) = 4n − 5, for all integers n.

(i) Is g one-to-one? Prove or give a counterexample.

(ii) Is g onto? Prove or give a counterexample.

b. Define G: R → R by the rule G(x)= 4x − 5 for all real numbers x .Is G onto? Prove or give a counterexample.

(For Reference) Chapter 2 pg 21-24 Classiﬁcation of motor skills- how we learn movement is a complex phenomenon Generalization of principals- a skill in one sport may cross over to another (following through in tennis, baseball, and basketball) Environmental predictability (not all of these fall strictly into one category) - open skill (unpredictable environment)return of serve, block, pass -closed skill (predictable environment)free throw, penalty kick, tennis serve Task organization -Discrete skill (beginning and end of skill are well deﬁned)(tend to be individual sports skills) A single soccer kick, a tennis serve, a baseball pitch. -Serial skill (combination of any skills) (tend to be entire games) Gymnastics routi