anonymous
  • anonymous
Construct examples a. show that if f and g are one to one, then f+g might not be one-to-one. b. show that if f and g are onto, then f+g need not be onto. c. give an example of functions f and g that are one to one and onto, but f times g is not one to one and not onto.
Mathematics
jamiebookeater
  • jamiebookeater
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zzr0ck3r
  • zzr0ck3r
how many times are you going to ask this question?
perl
  • perl
part a) hint: pick a one to one function for f, it can be any. then for g pick its negative. if you add them what do you get?
perl
  • perl
For example f(x) = e^x + 1 g(x) = -e^x both functions are one to one. What happens when you add the functions

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perl
  • perl
Actually a simpler function is f(x) = x g(x) = -x f and g are both one to one and onto. However f(x) + g(x) = 0 which is a constant function. The constant function is neither one to one nor onto.
perl
  • perl
f times g is neither one to one nor onto as well
zzr0ck3r
  • zzr0ck3r
@perl the user keeps posting the question under many different names, and refuses to take part

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