Define H: R R R R as follows: H(x, y) = (x + 1, 2 y) for all (x, y) R R. a. Is H

Chapter 7, Problem 29

(choose chapter or problem)

Define H: \(\mathbf{R} \times \mathbf{R} \rightarrow \mathbf{R} \times \mathbf{R}\) as follows:

H(x, y) = (x + 1, 2 − y) for all \((x, y) \in \mathbf{R} \times \mathbf{R}\).

a. Is H one-to-one? Prove or give a counterexample.

b. Is H onto? Prove or give a counterexample.

Text Transcription:

mathbf R times mathbf R rightarrow mathbf R times mathbf R

(x, y) in mathbf R times mathbf R