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Math Help - How to solve f(x) equations

  1. #1
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    Unhappy How to solve f(x) equations

    Hi How do I approach the question below:

    Let f(x)= 2x^2 - 5,g(x)= 3-4x, k(x) = 6x/(x^2-2)

    Find the following and simplify:

    a)g(-1)

    b) (g+k)(1)

    c)(fk)(2)

    d f(g(1)

    e (f(x+h) - f(x))/h

    I am extremely rusty.Can anyone help me solve these.Give me leads


    For instance for a)g(-1)

    Do I substitute 1 into the equation: g(x)= 3-4x

    Thanks
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  2. #2
    Senior Member abhishekkgp's Avatar
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    Re: How to solve f(x) equations

    Quote Originally Posted by KayPee View Post
    Hi How do I approach the question below:

    Let f(x)= 2x^2 - 5,g(x)= 3-4x, k(x) = 6x/(x^2-2)

    Find the following and simplify:

    a)g(-1)

    b) (g+k)(1)

    c)(fk)(2)

    d f(g(1)

    e (f(x+h) - f(x))/h

    I am extremely rusty.Can anyone help me solve these.Give me leads


    For instance for a)g(-1)

    Do I substitute 1 into the equation: g(x)= 3-4x
    No, you have to substitute -1 in the equation g(x)=3-4x. so g(-1)=3-4*(-1)=7.
    Thanks
    ...
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  3. #3
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    Re: How to solve f(x) equations

    So b) (g+k)(1)

    I have to add 7 to 6x/(x^2-2) and multiply by 1?
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  4. #4
    Senior Member abhishekkgp's Avatar
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    Re: How to solve f(x) equations

    Quote Originally Posted by KayPee View Post
    So b) (g+k)(1)

    I have to add 7 to 6x/(x^2-2) and multiply by 1?
    (g+k)(1)=g(1)+k(1). g(1) is not 7. g(1)=-1. (why?)
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  5. #5
    MHF Contributor Siron's Avatar
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    Re: How to solve f(x) equations

    d) If you have to simplify:
     f[g(1)], calculate g(1)=3-4.1=-1 and now you'll get: f(-1)=...?
    e) If you have to simplify:
    \frac{f(x+h)-f(x)}{h} and you know: f(x)=2x^2-5, then substitute the given into the equation:
    \frac{[2(x+h)^2-5]-[2x^2-5]}{h}=\frac{2x^2+4xh+2h^2-5-2x^2+5}{h}=...
    Last edited by Siron; August 6th 2011 at 12:28 PM.
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  6. #6
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    Re: How to solve f(x) equations

    I got it g(x)=3-4x
    g(1)=3-4
    =-1

    in that same vein
    k(1)=6/-1=-6
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  7. #7
    MHF Contributor Siron's Avatar
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    Re: How to solve f(x) equations

    Quote Originally Posted by KayPee View Post
    I got it g(x)=3-4x
    g(1)=3-4
    =-1

    in that same vein
    k(1)=6/-1=-6
    Right!

    Can you solve your exercices now? ...
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  8. #8
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    Re: How to solve f(x) equations

    b)(g+k)(1)=g(1)+k(1)
    =-1+(-6)=-7

    Hope I am right?
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  9. #9
    MHF Contributor Siron's Avatar
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    Re: How to solve f(x) equations

    Correct!
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  10. #10
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    Re: How to solve f(x) equations

    Any clues as to how I should approach parts (c) and (e) ?
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  11. #11
    MHF Contributor Siron's Avatar
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    Re: How to solve f(x) equations

    Use:
    (fk)(2)=f(2)\cdot k(2)
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  12. #12
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    Re: How to solve f(x) equations

    Quote Originally Posted by Siron View Post
    d) If you have to simplify:
     f[g(1)], calculate g(1)=3-4.1=-1 and now you'll get: f(-1)=...?
    e) If you have to simplify:
    \frac{f(x+h)-f(x)}{h} and you know: f(x)=2x^2-5, then substitute the given into the equation:
    \frac{[2(x+h)^2-5]-[2x^2-5]}{h}=\frac{2x^2+4xh+2h^2-5-2x^2+5}{h}=...
    for part d)I got f(-1)=2-5=-3
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  13. #13
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    Re: How to solve f(x) equations

    f(2)=3
    k(2)=6

    answer for (fk)(2)=18 ?
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  14. #14
    MHF Contributor Siron's Avatar
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    Re: How to solve f(x) equations

    Quote Originally Posted by KayPee View Post
    for part d)I got f(-1)=2-5=-3
    Correct!

    EDIT: c) is also correct.
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  15. #15
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    Re: How to solve f(x) equations

    Quote Originally Posted by KayPee View Post
    for part d)I got f(-1)=2-5=-3
    I guess for e I cannot arrive at a single figure .It just has to be simplified like you have done right?
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