f(x) = 6 / 5+x

Question

g(x) = f(f(x))

find a formula in terms of x ,for g^-1(x)

Answer 1

f(f(x))
= f(6/(5+x) )
= 6/(5 + 6/(5+x) )
= 6/( (25+5x+6)/(5+x) )
= (30 + 6x)/(31 + 5x) = g(x)

let y = (30+6x)/(31+5x)
inverse is :
x = (30+6y)/(31+5y)
31x + 5xy = 30 + 6y
5xy - 6y = 30 - 31x
y(5x - 6) = 30-31x
y = (30-31x)/(5x-6) = g^-1 (x)