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Math Help - [SOLVED] Functions

  1. #1
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    Red face [SOLVED] Functions

    Given f(x)= x^2 -2x +7 and  g(x)= 2x-3

    find a. (f+g)(2)

    b. (f.g)(2)

    c. (f/g)(2)

    d. (f.g)(x)

    Thanks in advance. I don't even know where to start
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  2. #2
    MHF Contributor red_dog's Avatar
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    (f+g)(2)=f(2)+g(2)

    (fg)(2)=f(2)g(2)

    \left(\frac{f}{g}\right)(2)=\frac{f(2)}{g(2)}

    (fg)(x)=f(x)g(x)
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  3. #3
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    I got it. I just need to substitute 2
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  4. #4
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    Quote Originally Posted by princess_21 View Post
    I got it. I just need to substitute 2
    For the parts where you're evaluating at 2, yes, you can plug "2" in for "x", evaluate, and then do the mathematical operations.

    For the part where you're "evaluating" at x, you'll need to work with the functions directly. But the operations on functions work the exact same way: Take the formulas, and do the operations with the polynomials or whatever, instead of which the numbers.

    In this case, you'll be multiplying the two polynomials to get the answer.

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  5. #5
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    ]am I doing it right??

    f(x)=x^2-2x+7

    g(x)=2x+3

    a. (f+g)(2)

    x^2-2x+7+2x-3

    x^2+4

    2^2 +4

    8

    b. (f.g)(2)

    2x^3-3x^2-4x^2+6x+14x-21

    2x^3-7x^2+20x-21

    2(2)^3+20(2)-21

    16-28+40-21

    7

    c. (\frac{f}{g})(2)

    \frac{x^2-2x+7}{2x-3}

    \frac{4-4+7}{4-3}

    7

    d. (FoG) =>the sign looks like a small "o"

    do this also means f(g(x)) if it is then I answered. ( i replaced x in f(x) using g(x) is this right??

    f(x)=x^2-2x+7

    (2x-3)^(2)-2(2x-3)+7

    4x^2-16x+22

    am i in the right track?? thanks for all your help
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  6. #6
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    Quote Originally Posted by princess_21 View Post
    f(x)=x^2-2x+7

    g(x)=2x+3

    a. (f+g)(2)

    x^2-2x+7+2x-3
    Where did the "-3" come from? From what you did later, I will guess that the original function (posted above) is typoed, and that g(x) should be "2x - 3". If so, then your value here is correct.


    Quote Originally Posted by princess_21 View Post
    b. (f.g)(2)

    ...

    7
    Since f(2) = 7 and g(2) = 1 (assuming the correction above is correct), then f(2)*g(2) = (7)(1) = 7, so your answer is correct.


    Quote Originally Posted by princess_21 View Post
    c. (\frac{f}{g})(2)

    \frac{x^2-2x+7}{2x-3}

    \frac{4-4+7}{4-3}

    7
    Since f(2)/g(2) = 7/1 = 7, then your solution value is correct.


    Quote Originally Posted by princess_21 View Post
    d. (FoG) =>the sign looks like a small "o"

    do this also means f(g(x))
    Yes; the raised "o" indicates the composition of functions. (I will guess that you mean "F" and "f" to mean the same function, as well as "G" and "g".)

    Quote Originally Posted by princess_21 View Post
    f(x)=x^2-2x+7

    (2x-3)^(2)-2(2x-3)+7

    4x^2-16x+22
    That's exactly right!
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  7. #7
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    whoa!! thanks..
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