Prove that if a(x) = |r|, the absolute value function, then a E C(R). (Use 1.9.)

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2.20
† Prove that if a(x) = |x|, the absolute value function, then a E C(R). (Use
Exercise 1.9.)
For reference:
1.9 † Prove: For all a and b in R,
|la| – l6|| < la – bl.
Intuitively, this says that la| and |b| cannot be farther apart than a and b are. (Hint:
Write |a| = |(a – b) + b| and use the triangle inequality. Then do the same thing for
|6|.)
Transcribed Image Text:2.20 † Prove that if a(x) = |x|, the absolute value function, then a E C(R). (Use Exercise 1.9.) For reference: 1.9 † Prove: For all a and b in R, |la| – l6|| < la – bl. Intuitively, this says that la| and |b| cannot be farther apart than a and b are. (Hint: Write |a| = |(a – b) + b| and use the triangle inequality. Then do the same thing for |6|.)
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