Question 465530: Find the domain of f(g(x)) given f(x)=x/x+8 and g(x)=16/x+3. Thank you, all of you do a wonderful service!!! Answer by lwsshak3(11628) (Show Source):
You can put this solution on YOUR website! Find the domain of f(g(x)) given f(x)=x/x+8 and g(x)=16/x+3.
...
f(x)=x/(x+8)
g(x)=16/(x+3)
..
f[g(x)]=f[16/(x+3)]
f[g(x)]=[16/(x+3)]/[16/(x+3)+8]
LCD:(x+3)
f[g(x)]=16/(16+8x+24)
f[g(x)]=16/(8x+40)
Finding domain:
restrictions are found in the denominators of g(x) and f[g(x)]:
set denominators=0
8x+40=0
8x=-40
x≠-5
..
x+3=0
x≠-3
..
Domain: (-∞,-5) U (-5,-3) U (-3,∞)
(