Suppose that the functions g and h are defined as follows gx

Suppose that the functions g and h are defined as follows. g(x) = 9/x, x notequalto 0 h (x) = x^2 - 6 Find the compositions g o g and h o h. Simplify your answers 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.)

Solution

g(x)=9/x, h(x)=x^2-6

gog(x)=g(g(x))

         =g(9/x)

         = 9/(9/x)=x

Therefore gog(x)=x

And hoh(x)=h(h(x))

                = h(x^2-6)

                =(x^2-6)^2 - 6

               =x^4+36-12x^2-6

              =x^4 + 30-12x^2

hoh(x)          = x^4-12x^2+30