Define f : R → R and g : R → R by the rules f(x) = 3x – 2 for allx2 +3 for all x E R.x E R and g(x) =(i) Is ƒ one-to-one? Prove or give a counterexample.(ii) Is g one-to-one? Prove or give a counterexample.

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Define f : R → R and g : R → R by the rules f(x) = 3.x – 2 for all x E R and g(x)= x² +3 for all x E R. (i) Is f one-to-one? Prove or give a counterexample. (ii) Is g one-to-one? Prove or give a counterexample.

Define f : R → R and g : R → R by the rules f(x) = 3.x – 2 for all x E R and g(x)= x² +3 for all x E R. (i) Is f one-to-one? Prove or give a counterexample. (ii) Is g one-to-one? Prove or give a counterexample.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

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Define f : R → R and g : R → R by the rules f(x) = 3x – 2 for all
x2 +3 for all x E R.
x E R and g(x) =
(i) Is ƒ one-to-one? Prove or give a counterexample.
(ii) Is g one-to-one? Prove or give a counterexample.

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