College Algebra! help!
posted by Rosie on .
Consider the following functions
f(x)= (7x+8)/(x+3) and g(x)= (3x8)/(7x)
(a) Find g(g(x))
(b) Find g(f(x))
(c) Determine whether the functions f and g are inverses of each other.

a)
g(g(x))
= g((3x8)/(7x)
= [3(3x8)/(7x)  8]/( 7  (3x8)/(7x) )
= [ (9x2456+8x)/(7x)] / (497x3x+8)/(7x)]
= (17x  80)/(57  10x)
b) do this in the same way I just showed you
c) let's take the inverse of f(x)
let y = (7x+8)/(x+3)
for the inverse, interchange the x and y
x = (7y+8)/(y+3)
xy + 3x = 7y + 8
xy  7y = 83x
y(x7) = 83x
y = (83x)/(x7) = (3x  8)/(7  x) = g(x)
yes , they are inverses of each other.