Question

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?

Answer 1

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