SOLUTION: 1. Find the domain of the composite function f◦g . Please show all of your work. f(x) = x + 6; g(x) = 7/x+7 Will someone help me with this problem? thank you.

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: 1. Find the domain of the composite function f◦g . Please show all of your work. f(x) = x + 6; g(x) = 7/x+7 Will someone help me with this problem? thank you.      Log On


   

Question 470264: 1. Find the domain of the composite function f◦g . Please show all of your work.
f(x) = x + 6; g(x) = 7/x+7

Will someone help me with this problem? thank you.
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
fog(x) is equal to f(g(x)).
this is described as f of g of x.
you have:
f(x) = x + 6
g(x) = 7/(x+7)
replace the x in f(x) with g(x)) to get:
f(g(x)) = 7/(x+7) + 6
that's your equation.
fog(x) = 7/(x+7) + 6
another example might clarify this a little better.
suppose f(x) = 5x^2 - 3x + 2
suppose g(x) = sqrt(x).
you want to find fog (x)
you replace x with g(x)) in your f(x) equation to get:
f(g(x)) = 5*(sqrt(x))^2 - 3*sqrt(x) + 2
you replace the x with sqrt(x) everywhere you had an x in the f(x) equation.
your equation becomes f(g(x)) = 5*x - 3*sqrt(x) + 2
note that sqrt(x)^2 is equal to x.