Let f(x) = (x+1)/(x+9). Then f^(-1)(-2) = ?

Question

Can anyone help me and include step-by-step procedures? Thank yoU!

Answer 1

looks seriously as if that numerator is going to equal zero at some point quite early in calculations,making f(-1)*f(-2) equal to zero in my book...but there MUST be a trick...

Answer 2

Some people will tell you that you need to find the inverse of f(x) in order to answer this question. That's actually not true. You can use the cancellation laws. Basically:

f(f^-1(x)) = x, and

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

for all x. We use the first one. Let a = f^-1(-2):

f(a) = -2

(a + 1) / (a + 9) = -2

a + 1 = -2(a + 9)

a + 1 = -2a - 18

3a = -19

a = -19/3

There's your answer: f^-1(-2) = -19/3