Chris Phan Tuesday, 27 January 2004
Math 111 Quiz #3
Solutions to Quiz #3
Again, there may be more than one way to solve these problems.
1. True. See āCautionā box on p. 139.
2. False. We have two outputs for ā1.
3. False. See āCautionā box on p. 139.
4. True. It is okay for a function two give the same output for two different inputs.
5. False. See āCautionā box on p. 139.
6. The function is undefined (in other words, its rule doesnāt make sense) when xā1<0. So the function
needs xā1ā„0, in other words xā„1, to be defined. Note I used āā„ā, not ā>ā, since ā0is defined.
Furthermore, the function needs x6=ā1, but that doesnāt actually make any difference, since we need
xā„1anyway. So, in interval notation (which I asked for), the domain is [1,ā).
7. Be sure to understand what g(x+h)means. (See āCautionā box on p. 136. We have
g(x+h)āg(x)
h=(x+h)2+ 3 ā(x2+ 3)
h
=x2+ 2xh +h2+ 3 āx2ā3
h
=2xh +h2
h= 2x+h.
8. The identify function is f(x) = x. Catalog of basic functionsāas my high school chemistry teacher
used to say: learn it, live it, love it!
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