a. Define H: R R by the rule H(x) = x 2, for all real numbers x. (i) Is H one-to-one
Chapter 7, Problem 13(choose chapter or problem)
a. Define H: \(\mathbf{R} \rightarrow \mathbf{R}\) by the rule \(H(x)=x^{2}\), for all real numbers x.
(i) Is H one-to-one? Prove or give a counterexample.
(ii) Is H onto? Prove or give a counterexample.
b. Define K: \(\mathbf{R}^{\text {nonneg }} \rightarrow \mathbf{R}^{\text {nonneg }}\) by the rule \(K(x)=x^{2}\), for all nonnegative real numbers x. Is K onto? Prove or give a counterexample.
Text Transcription:
mathbf R rightarrow mathbf R
H(x)=x^2
mathbf R^nonneg rightarrow mathbf R^nonneg
K(x)=x^2
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