SOLUTION: Suppose that the functions g and h are defined as follows. g(x) = 4/x, x is not 0 h(x) = x^2 -8 Find the compositions of g o g and h o h simplify your answers as muc

Algebra ->  Permutations -> SOLUTION: Suppose that the functions g and h are defined as follows. g(x) = 4/x, x is not 0 h(x) = x^2 -8 Find the compositions of g o g and h o h simplify your answers as muc      Log On


   

Question 1070731: Suppose that the functions g and h are defined as follows.

g(x) = 4/x, x is not 0
h(x) = x^2 -8
Find the compositions of g o g and h o h
simplify your answers as much as possible.
(g o g)( x) = _____
(h o h)(x) = ______
simplify your answer as much as possible.
(Assume that your expressions are defined for all x in the domain of the composition. You do not have to indicate the domain).


Answer by rothauserc(4718) About Me  (Show Source):
You can put this solution on YOUR website!
(g o g)(x) = 4 / (4/x) = 4x / 4 = x
:
(h o h)(x) = (x^2 - 8)^2 - 8 = x^4 -16x^2 +64 - 8 = x^4 -16x^2 +56 =
:
(x^2 - 10.8285) * (x^2 - 5.1715)
: