functions

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For each problem, construct two composite functions, . Evaluate each composite function for x=2

ok i have not dealt with composite functions can I please get some help with this as I have 20 questions to do can someone show me step by step on how to properly solve this equation is their a trick to doing this

f(x)x+1 g(x)=X^2+2x+1

  • functions -

    how can you possibly have an assignment working with something you have not studied?

    If you have f(x) and g(x) as functions, then there are two simple composite functions:

    f(g(x)) and g(f(x))

    Given your functions,
    f(g) = g+1 = (x^2+2x+1)+1 x^2+2x+2
    g(f) = f^2+2f+1
    = (x+1)^2 + 2(x+1) + 1
    = x^2+4x+4

    Check the related problems below to see other worked examples. Wouldn't hurt to check your class text, either, so you will have "dealt" with them.

    google will also turn up a wealth of examples.

  • functions -

    I will assume you defined you first function as
    f(x) = x+1
    also g(x) = x^2 + 2x + 1

    the simple ones are where you do one of the arithmetic operations
    e.g.
    (f+g)(x) = (x+1) + (x^2 + 2x + 1)
    = x^2 + 3x + 2

    similarly (g/f)(x) = (x^2+2x+1)/(x+1)

    etc

    the more complicated ones would be something like
    f(g(x) )
    = f(x^2+2x+1)
    = (x^2+2x+1) + 1 = x^2 + 2x + 1

    but

    g(f(x) ) = g(x+1)
    = (x+1)^2 + 2(x+1) + 1 . etc

    sometimes you will see this

    (f o g)(x) , it is simply another way to write f(g(x))
    notice that (g o f)(x) would be g(f(x) )

    hope this will get you going.

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