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Math Help - Composition of Functions

  1. #1
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    Composition of Functions

    I need help understanding whats going on...

    Let f(x)=(x^2)-1 and g(x)=3x.

    Find f * g.

    1.(f * g)(x)=f(g(x))
    2.---------=f(3x)
    3.---------=((3x)^2)-1
    4.---------=(9x^2)-1

    I primarily dont understand line 3. How can 3x((x^2)-1)=((3x)^2)-1 ?

    Perhaps you have a better way of explaining.


    Trying to teach myself Algebra 2.
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  2. #2
    MHF Contributor red_dog's Avatar
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    f(g(x))=f(3x)=(3x)^2-1=9x^2-1
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  3. #3
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    I can see that. I just dont understand the third line of my original post.

    How do they get to that conclusion?
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  4. #4
    MHF Contributor red_dog's Avatar
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    f(3x) means that in the function expression x is replaced by 3x.
    So f(3x)=(3x)^2-1, not 3x^2-1
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  5. #5
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    Quote Originally Posted by ceasar_19134 View Post
    I need help understanding whats going on...

    Let f(x)=(x^2)-1 and g(x)=3x.

    Find f * g.
    (f\circ{g})(x)=[g(x)]^2-1

    But g(x)=3x, so (f\circ{g})(x)=(3x)^2-1={\color{blue}9x^2-1}~\blacksquare

    Did you get it now?
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  6. #6
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    Okay I get line 3 now, but how did you get (9x)^2 out of (3x)^2?
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  7. #7
    Grand Panjandrum
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    Quote Originally Posted by ceasar_19134 View Post
    Okay I get line 3 now, but how did you get (9x)^2 out of (3x)^2?
    Nobody has got (9x^2) from (3x^2) what they
    have done is: (3x)^2=(3)^2(x)^2=9x^2

    RonL
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