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Composition of functions - find range

  1. Dec 26, 2006 #1
    Good evening guys, i have two stupid questions that i'm stuck on and i would be grateful if anyone could help

    Question 1:

    f(x)= x+1 g(x)=x^2

    the domain in each case is the interval [-1,1] and belongs to the set of real numbers then find the range of:

    (fog)(x)

    My Answer:

    i found (fog) to be x^2 +1 then i put in -1,0 and 1 to get the range

    or should i do (fog)*(x) which would make it x^3 + x

    Question 2:

    determine which of the following questions are equal:

    f:{1} -> N (the set N) and g:R-> R (the set R) be functions given by

    f(x)=x-1 and g(x)=0

    My Answer

    f(x) not equal g(x)

    because 0 doesn't belong to the set N ?

    (i feel so dum asking these questions!)
     
  2. jcsd
  3. Dec 26, 2006 #2

    cristo

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    correct
    No, (fog)(x) means f(g(x)), so you do as you did above.. apply g to the x, then apply f to g(x)

    correct
    No need to feel dumb: the only way to learn is to ask questions!
     
  4. Dec 26, 2006 #3
    thanx cristo!
     
  5. Dec 26, 2006 #4

    matt grime

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    what do you mean by 'question'? And what do you mean by 'which of them are equal'? Sorry, but that sentence doesn't make any sense, and I can't guess at what you mean.

    well, those are two obviously unequal *functions*, since they have different domains and ranges. (And it is moot whether or not 0 is or is not in N.)

    If 0 is not in your set N, then f is not even a properly defined function.

    Even 'which of the following functions are equal?' doesn't make sense.
     
    Last edited: Dec 26, 2006
  6. Dec 26, 2006 #5
    the question refers to the different parts of it

    i.e determine which of the following questions are equal:

    a)f:{1} -> N (the set N) and g:R-> R (the set R) be functions given by

    f(x)=x-1 and g(x)=0

    b) (another one)

    c) (another one)

    i left the question in plural form to avoid confusion...looks like i did the opposite.

    also i was asking if 0 belonged to the set N...but now i know that it does and that the function f and g are not equal because they have different domains and co domains thanx to you.

    '(And it is moot whether or not 0 is or is not in N.)'

    what does moot mean?
     
  7. Dec 26, 2006 #6

    matt grime

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    This still doesn't make any sense. Even if you're to acutally put three parts to the question in it will not make sense. There are no questions at all, and it would be strange to ever ask when questions are equal.



    But surely you just have to read the sentence you wrote to understand that I'm not making any comment on mathematics. It genuinely is not something that made sense, nor does it even now.

    It would be strange if the question actually asked 'are *those* two functions equal', because they clearly are not equal functions. Hence my continued confusion. And your answer that 0 was not in N didnt' help me work out what it was that you were trying to answer. It is very important to actually write the question you were asked, not what you think you were asked so that people can help.

    If you're ever not sure of the meaning of a word, and a dictionary is not to hand, then you can either google for the meaning (there are lots of free dictionaries on the web), or just google the word itself, then in the slightly blue bar going across the screen above the results the words you searched for are listed, with links to definitions of all the words. I realise it would be shorter to actually define it for you, but this is useful information. There is no reason to ever be in doubt abuot the meaning of a word.
     
    Last edited: Dec 26, 2006
  8. Dec 26, 2006 #7
    determine which of the following 'questions' are equal
    damn i meant functions! not questions!

    now it makes sense doesn't it?

    even though i wrote the qusetion wrong and you said that it 'doesn't make any sense' you still managed to answer it for me...cheers!
     
  9. Dec 26, 2006 #8

    matt grime

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    Had I known that was precisely what the question asked, then I would have been duty bound *not* to have answered as I did. I didn't believe that they would actually ask that question of *those* two functions.
     
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