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March 29, 2017

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h(x)=5/x^2+6
I know the answer is: f(x)=x+6, g(x)=5/x^2, but I do not know how to get it. Can someone help me understand it?

  • Algebra - ,

    First break it down
    x=x+6 and x=5/x^2
    x=-1 x=2.5

  • Algebra - ,

    You did not state the question.
    Is it
    h of f of g of x = 5/x^2 + 6 ?

    There is surely more than one answer you can find by trial and error. For example another might be:
    try g(x) = 1/x^2
    then f(x) = 5 x
    then f (g) = 5 (1/x^2) = 5/x^2 which is what I want except I have to add 6
    so say h(x) = x + 6
    then h (f) = 5/x^2 + 6
    so the sequence
    g(x) = 1/x^2
    f(x) = 5 x
    h(x) =x + 6
    also yields
    h(x) = 5/x^2 + 6

  • Algebra - ,

    Consider the function h as defined. Find functions f and g so that
    (f o g)(x)=h(x)

    h(x)=5/x^2+6

  • Algebra - ,

    oh
    then I would modify that answer:

    There is surely more than one answer you can find by trial and error. For example another might be:
    try g(x) = 1/x^2
    then f(x) = 5 x + 6
    then f (g) = 5 (1/x^2) +6 = 5/x^2 + 6
    then h (f) = 5/x^2 + 6
    so the sequence
    g(x) = 1/x^2
    f(x) = 5 x + 6
    also yields
    h(x) = 5/x^2 + 6

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