Find the compositions: hoh and fof

Question

Suppose the functions h and f are defined as follows:

 

h(x)=8/x, x not equal sign 0

f(x)=x^2-8

 

(hoh)(x)=

(fof)(x)=

 

Please Find the compositions hoh and fof.

Simplify 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.

Thank you very much

Answer 1

h(x) =8/x

(hoh)(x) = h(h(x)) = h(8/x) = 8/(8/x) = 8(x/8) = x

(hoh)(x) = x

f(x) = x^2 - 8

(fof)(x) = f(f(x)) = f(x^2-8) = (x^2-8)^2 - 8 = x^4 - 16x^2 + 64 -8 = x^4 -16x^2 + 56

(fof)(x) = x^4 -16x^2 +56