Algebra

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For the given functions f and g find the following and state the domain of each result f(x)=5x+1/4x-7; g(x) = 3x/4x-7

  • Algebra -

    find the following what?
    Domain of f and g is all reals except x=7/4

  • Algebra -

    a) (f+g)(x)=
    what is the domain of f+g?

    b) f/g(x)=
    What is the domain of f/g?

  • Algebra -

    since f and g have the same domain, f+g has the same domain as f and g.

    f/g = (5x+1)/(3x)
    Now, we have to exclude x=7/4 because neither f nor g is defined there.
    In addition, we have to exclude x=0 because f/g is not defined there.
    So, domain of f/g is all reals except 0,7/4

  • Algebra -

    f+g(x)=?

  • Algebra -

    eh? Just add 'em up:

    (f+g)(x)
    = f(x)+g(x)
    = (5x+1)/(4x-7) + 3x/(4x-7)
    = (5x+1+3x)/(4x-7)
    = (8x+1)/(4x-7)

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