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Math Help - a lot of confusion about Functions!!

  1. #1
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    galway
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    a lot of confusion about Functions!!

    consider the following functions

    a lot of confusion about Functions!!-maths.png

    I have attached a screen shot of my problem as that was easier than typing it out.

    Apologies if this is posted in the wrong section, i have to do this problem by Thursday and to be honest i don't really have a clue but its important i get this right. anyway ill take a stab at it and hopefully some more experienced people can set me right.

    so for the first part with the graph i need to get f(x) = g(x)
    which would look something like this


    f(x)=x2-1
    g(x)=x+1

    f(x) = g(x)
    x2-1=x+1
    (x+1)-(x2-1)=o
    (x+1)-x2+1=0
    -x2+x+2=0


    S0 from here i need to get some co-ordinates from the above equation so i can use to draw a line on the graph?? i think, im not really sure where to go from here....and my maths may even be way off here like i said im unsure

    moving on to next section
    compute the following values:
    f(2)
    g(0)
    f(2/3)


    f(2)=(2)2-1 = 4-1=3
    g(0)=(0) +1=1
    f(2 over 3)= (2 over 3)2+1= ??

    i think the first two may be right not sure what to do with fraction in last one.

    as for the last section

    f dot g (x) = f(x+1)=(x+1)2-1
    g dot f (x) = g(x2-1) = (x2-1)+1
    f dot (x) = f(x2-1) = (x2-1)2-1
    g dot g(x) = g(x+1)=(x+1) + 1

    again i think im right here? could some one confirm if i am or not

    I realize this is a long post i just want to thank anyone in advance who can lend me their expertise!
    Last edited by ronanbrowne88; October 22nd 2013 at 11:38 AM.
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  2. #2
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    Re: a lot of confusion about Functions!!

    Quote Originally Posted by ronanbrowne88 View Post
    so for the first part with the graph i need to get f(x) = g(x)
    which would look something like this

    f(x)=x2-1
    g(x)=x+1

    f(x) = g(x)
    x2-1=x+1
    (x+1)-(x2-1)=o
    (x+1)-x2+1=0
    -x2+x+2=0
    This is correct so far. I would recommend multiplying both sides of the equation by -1 and then trying to factor the polynomial.

    Quote Originally Posted by ronanbrowne88 View Post
    S0 from here i need to get some co-ordinates from the above equation so i can use to draw a line on the graph?? i think, im not really sure where to go from here....and my maths may even be way off here like i said im unsure
    That is correct. Making a table of values might help.

    Quote Originally Posted by ronanbrowne88 View Post
    moving on to next section
    compute the following values:
    f(2)
    g(0)
    f(2/3)

    f(2)=(2)2-1 = 4-1=3
    g(0)=(0) +1=1
    f(2 over 3)= (2 over 3)2+1= ??
    You are correct for the first two. For the last one, an exponent of 2 means multiply the number by itself. Do you remember how to multiply two fractions? I will set it up for you:

    f\left( \dfrac{2}{3}\right) = \left(\dfrac{2}{3}\right)^2+1 = \dfrac{2}{3}\cdot \dfrac{2}{3} + 1

    Quote Originally Posted by ronanbrowne88 View Post
    as for the last section ill i don't know how to even attempt it if anyone could show me how to do one as a example i can try the rest.

    I realize this is a long post i just want to thank anyone in advance who can lend me their expertise!
    The last section is composition of functions. So, (f\circ g)(x) means take the function f(x) and wherever you see an x, replace it with g(x). So, (f\circ g)(x) = f(g(x)) = (g(x))^2+1. Now, in place of g(x), put the formula for g(x).
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  3. #3
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    Re: a lot of confusion about Functions!!

    thanks for the advice, so continuing on with your advice in mind first section

    f(x)=x2-1
    g(x)=x+1

    f(x) = g(x)
    x2-1=x+1
    (x+1)-(x2-1)=o
    (x+1)-x2+1=0
    -x2+x+2=0
    -x2+x+2=0 (next multiply by -1)

    x2 -x -2 =0 (next factorize)

    x2−x−2=1(x−(−1))(x−2)
    x2−x−2=(x+1)(x−2)
    x1=−1
    x2=2

    then i can use these point to draw the graph. correct??

    the last one on part 2

    f(2 over 3)= (2 over 3)2+1= 4 over 9 +1 = 1 and 4 over 9 (sorry cant see a button to write in correct format)

    and last bit

    f dot g (x) = f(x+1)=(x+1)2-1
    g dot f (x) = g(x2-1) = (x2-1)+1
    f dot (x) = f(x2-1) = (x2-1)2-1
    g dot g(x) = g(x+1)=(x+1) + 1
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  4. #4
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    Re: a lot of confusion about Functions!!

    Quote Originally Posted by ronanbrowne88 View Post
    f(x)=x2-1
    g(x)=x+1

    f(x) = g(x)
    x2-1=x+1
    (x+1)-(x2-1)=o
    (x+1)-x2+1=0
    -x2+x+2=0
    -x2+x+2=0 (next multiply by -1)

    x2 -x -2 =0 (next factorize)

    x2−x−2=1(x−(−1))(x−2)
    x2−x−2=(x+1)(x−2)
    x1=−1
    x2=2

    then i can use these point to draw the graph. correct??
    Those points only tell you the x-coordinate where the two functions intersect. To graph the functions, you will want a table with more values for each function.


    Quote Originally Posted by ronanbrowne88 View Post
    the last one on part 2

    f(2 over 3)= (2 over 3)2+1= 4 over 9 +1 = 1 and 4 over 9 (sorry cant see a button to write in correct format)
    Seems we wrote down the wrong formula for f(x). At the top, you have f(x) = x^2-1, so it should be \dfrac{4}{9} - 1. Find a common denominator, and you can simplify.

    Quote Originally Posted by ronanbrowne88 View Post
    and last bit

    f dot g (x) = f(x+1)=(x+1)2-1
    g dot f (x) = g(x2-1) = (x2-1)+1
    Good, but you can simplify (g\circ f)(x) (-1+1 = 0).

    Quote Originally Posted by ronanbrowne88 View Post
    f dot (x) = f(x2-1) = (x2-1)2-1
    g dot g(x) = g(x+1)=(x+1) + 1
    You can also simplify (g\circ g)(x) (1+1 = 2).

    Other than that, everything looks great.
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  5. #5
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    Re: a lot of confusion about Functions!!

    great thanks!
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