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Math Help - composite functions with sine

  1. #1
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    composite functions with sine

    f(x) = sin (x)
    g(x) = x^2 - x + 1

    the question basically asks for a composite g o f, or g(f(x)). I get:

    = sin (x^2 - x + 1)
    = sin^2x - sin x + .... (i dont know how to multiply sin with 1, is it just sin(1) ?)

    its kinda confusing for me, since sine isn't really a variable, it's more like a "modifier" for a variable
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  2. #2
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    Quote Originally Posted by snypeshow View Post
    = sin (x^2 - x + 1)
    This is f(g(x)). You want g(f(x)).

    = sin^2x - sin x + .... (i dont know how to multiply sin with 1, is it just sin(1) ?)
    No, no, no and no. Never, EVER do that again. sin(x) is a function. It is not a modifier. Never, ever, split up its argument like that. Ever. "sin" means nothing - except in a religious sense. "sin" must have an argument.

    Didn't we do g(f(x)) already in the Domain and Range question?
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    Quote Originally Posted by TKHunny View Post

    Didn't we do g(f(x)) already in the Domain and Range question?
    the domain and range question was multiplying 2 functions. this question is about composite functions.

    Composite functions are when you have 2 functions (so f(x) and g(x)) and f o g means that g(x) replaces x in the function f(x)

    so in the question, f(x) = sin x and g(x) = x^2 - x + 1
    I'm looking for f(g(x)) (sorry, i said the opposite in my first post, my fault)

    so f(g(x)) = sin (x^2 - x + 1)

    how would i evaluate f(g(x))? or do i leave it as is?


    (and yeah i guess im not too good with trig, as you could probably tell )
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  4. #4
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    No worries. Just pin down what the notation means.

    Quote Originally Posted by snypeshow View Post
    so f(g(x)) = sin (x^2 - x + 1)
    Good.

    How would i evaluate f(g(x))? or do i leave it as is?
    There is some push to "simplify". "Evaluate" really doesn't mean much.
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    Quote Originally Posted by TKHunny View Post
    No worries. Just pin down what the notation means.

    Good.

    There is some push to "simplify". "Evaluate" really doesn't mean much.
    so f(g(x)) = sin (x^2 - x + 1) can't be broken down any more right?
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  6. #6
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    bump

    and how would i find the domain and range for this question?
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  7. #7
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    Quote Originally Posted by snypeshow View Post
    so f(g(x)) = sin (x^2 - x + 1) can't be broken down any more right?

    Using the trig identity

    \sin(a + b) = \sin a \cos b + \cos a \sin b

    you have

    \sin (x^2 - x + 1) = \sin ((x^2 - x) + 1) =

    \sin (x^2 - x) \cos 1 + \cos(x^2 - x) \sin 1

    and you can break that down even further using

    \sin(a - b) = \sin a \cos b - \cos a \sin b and

    \cos(a - b) = \cos a \cos b + \sin a \sin b
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  8. #8
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    thanks!

    I'm also looking for the domain and range for this function (specifically the range)
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  9. #9
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    Quote Originally Posted by snypeshow View Post
    thanks!

    I'm also looking for the domain and range for this function (specifically the range)
    What is the range of the sine function?
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