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  1. MHB Apprentice

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    #1
    The questions is asking me to find \frac{f}{g} basically , the question is asking me to find the answer , even though i know it, i can't get my head around it.

    the composite function is

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

    we need to find foG (f of g) [composite functions].

  2. MHB Apprentice

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    #2 Thread Author
    Quote Originally Posted by HelpPlease View Post
    The questions is asking me to find \frac{f}{g} basically , the question is asking me to find the answer , even though i know it, i can't get my head around it.

    the composite function is

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

    we need to find foG (f of g) [composite functions].
    Thank you solved.


    Divide them both so x^2+1 / 1/x
    switch them to multiply so it's gonna be x^2+1/x

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    #3
    $f \circ g(x)= f(g(x))=\frac{1}{x^2}+1$

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    #4
    Additionally, the quotient (which is not the composite $f \circ g$) is:
    $$\frac fg(x) = \frac{f(x)}{g(x)}=\frac{x^2+1}{1/x}=(x^2+1)x=x^3+x$$

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    #5
    Just to add an intermediary step:

    $ \displaystyle (f\circ g)(x)=f(g(x))=f\left(\frac{1}{x}\right)=\left(\frac{1}{x}\right)^2+1=\frac{1}{x^2}+1$

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