What is f(x) given that g(x) =x-1/x+2 and gof(x) =7/x+2?

Answer 1

g(x) = x - 1/(x+2)

g(f(x) = 7/(x+2)

f(x) = 2 or -4

g(2) = 2-1/(x+2) = 2-1/4 = 7/4

g(f(x) = 7/(2+2)= 7/4

g(-4) = -4-1/(-4+2) = -4-1/-2 = -4+1/2 =-7/2

g(f(x) = g(-4) =7/(-4+2) = 7/-2= -7/2