college algebra

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1.for the given function f&g, find the following and state the domain of each result.

f(x)=2x+1/9x-5; g(x) 4x/9x-5
a.(f+g)(x)=?
What is the domain?

b. (f/g)(x)=?
what is the domain?

2.the function f is defined as follows
{x+6 if -5 ¡Üx<1
f(x)={9 if x=1
{-x+4 if x>1

a. the domain of the function f is ?
b. what are the intercepts?

  • college algebra -

    on the second question it should be

    f(x)= {x+6 if -5is less than or greater than x<1
    9 if x=1
    -x+4 if x>1

    sorry it didn't come out right.

  • college algebra -

    it is customary online to use <= or >= for less than or equal, etc.

    for both f and g, the domain is all reals except x = 5/9
    so, f+g has the same domain

    f/g = (2x+1)/4x
    so, you would think the domain is all reals except x=0, but since neither f nor g is defined at x = 5/9, we have to exclude that as well.

    2.
    since all pieces of f are polynomials, their domain is just as stated: [-5,1)U(1)U(1,oo) = [-5,oo)
    intercepts: (0,6) and (4,0)

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