Advanced Functions

Question

Please, help me with this crazy question;

given f(x) = k(1+x), find the value of k in f^-1(-2)=9.

Answer 1

y = k(x+1)

switch x and y

x = k(y+1) solve for y

x/k = y+1

y = x/k-1

f^-1(x) = x/k -1

f^-1(-2) = -2/k -1 = 9

-2/k = 10

k =-2/10 = -1/5

k=-1/5 = -0.2