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 470281: 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.
Found 2 solutions by Theo, Gogonati:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
I previously answered this question but i didn't tell you what the domain was.
I gave you the answer that f(g(x)) = 7/(x+7) + 6
you got this by replacing the x in f(x) with g(x) which is equal to 7/(x+7).
the domain of this equation would be all real numbers except x = -7.
when x = -7, the denominator in the fraction becomes 0 which makes the value of the fraction undefined.
a graph of your f(g(x)) equation is shown below:
graph%28600%2C600%2C-10%2C10%2C-100%2C100%2C%287%2F%28x%2B7%29%29%2B6%29
if you draw a vertical line at x = -7, you will see that you have an asymptote there.

Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
First we get the composite function: f%28g%28x%29%29=7%2F%28x%2B7%29%2B6 <=>
f%28g%28x%29%29=%287%2B6%28x%2B7%29%29%2F%28x%2B7%29 <=> f%28g%28x%29%29=%286x%2B49%29%2F%28x%2B7%29.
This function is defined for x+7≠0 or x≠-7, and its domain will be:
(-infinity, -7)U (-7, infinity).