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Question:

zoesantos
zoesantos
Student
High School - 11th Grade

How do you solve functions that have fractions?

If f(x)=1/x and g(x)=x/1+x, how would you find each of the following:

(f+g)(x), (f-g)(x), (f*g)(x), (f/g)(x), (g.f)(x), and (f.g)(x)

I don't know where to begin when approaching functions with fractions in them. Please help me!

 

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Posted by zoesantos on Tuesday October 13, 2009 at 4:25 PM and tagged with composite, fractions, functions, math, variables.

Answers:

  1. kjcdb8er
    kjcdb8er Teacher

    eNotes Editor

    (f+g)(x) is like saying f(x) + g(x); (f/g)(x) is like saying f(x)/g(x), and so on. (g.f)(x) is like saying g(f(x)).

    So,

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

    To add fractions, make the denominators equal, like this:

    1/x + x/(1+x) = (1/x)*(1 + x)/(1 + x) + x/(1 + x)*(x/x)

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

    See how the denominators are now the same? So we can combine:

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

     

    (f-g)(x) is the same, just with a minus sign: f(x) - g(x):

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

     

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

     

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

     

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

     

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

    Sources:
    http://www.enotes.com/math/q-and-a/given-f-x-5x-7-g-x-5x-...

    Rate answer:

    Posted by kjcdb8er on Tuesday October 13, 2009 at 5:10 PM