# Mathematical Thinking: Problem-Solving and Proofs (2nd Edition)

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1.7. The domain of the absolute value function is all of R since R = ( -∞ , 0] [0 , ). The image I is S = { x R : x 0 } . If x S , then | x | = x , so x I . If x / S , then x < 0, so | y | 6 = x for any y R since the definition of the absolute value function ensures that the absolute value function takes on only nonnegative values. Thus
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Unformatted text preview: x / ∈ I . It follows that I = S . 1.24. There is no missing dollar. Adding the tip to the amount the guests paid is erroneous. The charge for the room (\$25) plus the tip (\$2) coincide with the total amount paid by the guests (3 · \$9=\$27). 1...
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