Please help! Find the compositions: hoh and fof

Question

Suppose the functions h and f are defined as follows:

 

h(x)=2/x, x not equal sign 0

f(x)=x^2-6

 

(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)=2/x, x ≠ 0

 

(h o h)(x) = h(2/x) = 2/(2/x) = 2•(x/2) = x.  OBSERVATION: Therefore h is its own inverse!

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f(x)=x²-6  so  (hoh)(x)= (x²-6)² - 6  and I leave it to you to simplify this.