we need to find such x that f^-1(9) = x

f^-1(9) = x if and only if f(x) = -9

f(x) = -9

(x+1)/(x+9) = -9 multiply both sides by (x + 9)

x + 1 = -9(x + 9)

x + 1 = -9x - 81

x + 9x = -1 -81

10x = - 82 divide both sides by 10

x = - 8.2

f^-1(-9)= - 8.2 since f(8.2) = -9