Posted by anonymous on Wednesday, January 9, 2013 at 12:31am.
consider the function
f(x)=2x+8/x+6, g(x)=6x8/2x
a. what is f(g(x))?
b. give any vales of x that need to be excluded f(g(x)).
c. what is g(f(x))?
d. give any values of x that need to be excluded from g(f(x)).
e. Are the function f and g inverse of each other?

math  Steve, Wednesday, January 9, 2013 at 10:51am
f(g) = (2g+8)/(g+6)
= (2(6x8)/(2x)+8)/((6x8)/(2x)+6)
= x
f(6) is not defined, but since g(x) is never 6, the domain is all reals.
g(f) = (6f8)/(2f)
= (6(2x+8)/(x+6)8)/(2(2x+8)/(x+6))
= x
f and g are inverses since f(g) = g(f) = x