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Math Help - Find Composite Function Components

  1. #1
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    Find Composite Function Components

    Find functions f and g such that f (g) = H if H (x) = 1/(x + 1).
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by symmetry View Post
    Find functions f and g such that f (g) = H if H (x) = 1/(x + 1).
    Suppose f(x)=1/x, and g(x)=x+1, then:

    f(g(x))=f(x+1)

    then if y=x+1, we have f(g(x))=f(y)=1/y=1/(x+1),

    so H(x)=1/(1+x), as required.

    RonL
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  3. #3
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    ok

    Very impressive, Ron.

    Tell me, is finding composite function components required in calculus?
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by symmetry View Post
    Very impressive, Ron.

    Tell me, is finding composite function components required in calculus?
    I don't know I have never followed the US maths course sequence (we
    don't/didn't do things that way in the UK). As far as I recall we learned
    stuff as it was needed.

    Some knowledge of composite functions is needed for the chain rule, but
    as far as I recall a formal treatment of composite functions was not needed
    in the courses I pursued until the transition to university real analysis (1st
    year undergrad maths here).

    Maybe one of our US helpers will be able to answer your question better.

    RonL

    RonL
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  5. #5
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    ok

    So, you are from the UK? Interesting.

    Thanks!
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