Question

What are the chances that the inverse function of f(x) = (x+4)/(3-3x) is f^-1(x) = (3x-4)/(1-3x)? Explain.

Answer 1

Not so good!
If it would be the inverse, then f^-1(f(a))= a for every a.
If you put 2 in f, you get: f(2)=6/-3 = -2.
If you now calculate f^-1(-2), it is: (3*(-2)-4)/(1-3*(-2))=-10/7.

So f^-1(2)) is not equal to 2.
We can stop here. f^-1 is not the inverse of f.

Answer 2

Okay. Thanks.