Posted by **anonymous** on Wednesday, January 9, 2013 at 12:31am.

consider the function

f(x)=2x+8/x+6, g(x)=6x-8/2-x

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(6x-8)/(2-x)+8)/((6x-8)/(2-x)+6)

= x

f(-6) is not defined, but since g(x) is never -6, the domain is all reals.

g(f) = (6f-8)/(2-f)

= (6(2x+8)/(x+6)-8)/(2-(2x+8)/(x+6))

= x

f and g are inverses since f(g) = g(f) = x

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