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Math Help - Algebra Of Function Steps

  1. #1
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    Algebra Of Function Steps

    Hello,
    I have a couple of function problems that I have the answers to, but the steps shown in the book are confusing the heck out of me. Perhaps someone may be able to explain it a little more clearer.

    For the first one, it is asking me to find: (f+g)(x) and (f+g)(5) and apply them to:

    f(x)=3x+1, g(x)=2x-6


    Also, to these:

    f(x)=x-5, g(x) =3x^2

    Thanks!
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  2. #2
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    Re: Algebra Of Function Steps

    Quote Originally Posted by annon25 View Post
    Hello,
    I have a couple of function problems that I have the answers to, but the steps shown in the book are confusing the heck out of me. Perhaps someone may be able to explain it a little more clearer.

    For the first one, it is asking me to find: (f+g)(x) and (f+g)(5) and apply them to:

    f(x)=3x+1, g(x)=2x-6

    (f+g)(x) = f(x) + g(x) = (3x+1) + (2x-6) = 5x-5

    (f+g)(5) = 5(5)-5 = 20


    Also, to these:

    f(x)=x-5, g(x) =3x^2

    you try this one ...
    ...
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    Re: Algebra Of Function Steps

    Given two functions f,g:\mathbb{R}\to \mathbb{R} , we define a new function denoted by f+g in the following way:

    f+g:\mathbb{R}\to\mathbb{R}\;,\quad (f+g)(x)=f(x)+g(x)

    If you understand this definition you'll solve easily the problem.

    Edited: Sorry, I didn't see skeeter's post.
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  4. #4
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    Re: Algebra Of Function Steps

    I'm given the answer 75, but am coming up with a completely different one. Here are my steps

    (x-5)+(3x^2)=3x^2+x-5

    (5)(3^2)(5) = 225
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  5. #5
    MHF Contributor Amer's Avatar
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    Re: Algebra Of Function Steps

    (5-5) + ( 3 (5)^2) not (5)(3^2)(5)
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  6. #6
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    Re: Algebra Of Function Steps

    Quote Originally Posted by annon25 View Post
    Hello,
    I have a couple of function problems that I have the answers to, but the steps shown in the book are confusing the heck out of me. Perhaps someone may be able to explain it a little more clearer.

    For the first one, it is asking me to find: (f+g)(x) and (f+g)(5) and apply them to:

    f(x)=3x+1, g(x)=2x-6


    Also, to these:

    f(x)=x-5, g(x) =3x^2

    Thanks!



    Think of the distributive rule in terms of (f + g)(x).


    (f + g)(x) = f(x) + g(x).


    For the second question, we know that f(x) = x - 5 and g(x) = 3x^2.

    So, (f + g)(x) = x - 5 + 3x^2.


    Now we are told to replace x with 5 as indicated by (f + g)(5).

    Let x = 5 and plug into x - 5 + 3x^2.

    x - 5 + 3x^2

    5 - 5 + 3(5)^2

    0 + 3(25)

    0 + 75

    75 is the second answer.
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