Given that h(x)=x+1/x-2 and g(x) =4-x. Find h(g)(x) and find g(h)(x).

Question

P.S. Thanks for the correction Steve.

Answer 1

h(g) = (g+1)/(g-2)
= ((4-x)+1)/((4-x)-2)
= (5-x)/(2-x)

g(h) = 4-h
= 4 - (x+1)/(x-2)
= (4(x-2) - (x+1))/(x-2)
= (3x-9)/(x-2)