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F of g of x chart

  1. Jun 11, 2013 #1
    Hi, I just took a placement exam for college and I would like to go over some of the questions that I got wrong. There are quite a few but this one in particular keeps me wondering. I know how to do the regular f of g of x when functions are given but in this problem it is just a chart full of numbers. Any help will be greatly appreciated.
     

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  2. jcsd
  3. Jun 11, 2013 #2
    Check in which column x=5 and see what f(x) is in that column, you then know what f of 5 is, now find out what the g of f of 5 is by following the same procedure as you did for finding the f of x.
     
  4. Jun 11, 2013 #3
    So the answer would be 3?
     
  5. Jun 11, 2013 #4
    Oh sorry, you need to find the f of g of 5 (not the g of f of 5), my original post should have been:

    Check in which column x=5 and see what g(x) is in that column, you then know what g of 5 is, now find out what the f of g of 5 is by following the same procedure as you did for finding the g of x.
     
  6. Jun 11, 2013 #5
    So then -3?
     
  7. Jun 11, 2013 #6
    No, what is g(5)?
     
  8. Jun 11, 2013 #7
    Oh, -1? Sorry if it's wrong again I'm still a little confused on which rows to go to.
     
  9. Jun 11, 2013 #8
    No, to see what g(5) is, you should just check in which column x equals 5 and see what g(x) is in that column.
     
  10. Jun 11, 2013 #9

    MarneMath

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    Don't get ahead of yourself. What is g(5) based on that chart? Whatever number that is becomes your new 'x' and then find that number for f(x).
     
  11. Jun 11, 2013 #10
    So in the g column, where the 5 is, x=4. Is this the g(x) or am I still mixing it up?
     
  12. Jun 11, 2013 #11
    No, rows are horizontal, columns are vertical. The x row is the top row, move horizontally to where x=5, below that you see what f(x) is when x=5 and again one below you see what g(x) is when x=5
     
  13. Jun 11, 2013 #12
    Looking at the x row at the top I go to where x=5 then the f row shows -3 and the g row shows 3.

     
  14. Jun 11, 2013 #13
    Indeed, so f(5)=-3 and g(5)=3.

    You were asked "what is f(g(5))". Now that you know what g(5) is, call it b, you can find out what f(g(5)) is. It is equal to f(b).
     
  15. Jun 11, 2013 #14
    So where the g row states 5 right above it in the f row,which is -1.
     
  16. Jun 11, 2013 #15

    MarneMath

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    Ok so can we agree that g(5) = 3, right? So now you have f(g(5)) = f(3), makes sense?
     
  17. Jun 11, 2013 #16
    No, when solving f(g(5)), meaning f of g of 5, you go like this:
    First: What is g(5)? You saw g of 5 is 3, because when x=5 then g(x)=3.
    Next: what is f(g(5))... hmm, I know g(5)=3, so the question is: "what is f(3)?"
     
  18. Jun 11, 2013 #17
    Ohhh I think I get it now! So you go back to the top afterwards so it would be 2.
     
  19. Jun 11, 2013 #18
    Correct!
     
  20. Jun 11, 2013 #19
    Great! Thanks guys so much for all of the help.
     
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