Find (f o f ) (x)

Question

Hi, I need to know if my answer is right. 

 

f(x)=(3x+2)/(x-3). Find (f o f ) (x) . 

 

I got x. 

Answer 1

The reason that (f o f)(x) = x is because this function is its own inverse.

Answer 2

Lets check.

 

(f ο f)(x) =

 

f(f(x)) =

 

f[(3x + 2) / (x - 3)] =

 

[3((3x+2)/(x-3)) +2 / ((3x+2)/(x-3)) - 3]

 

 

Simplify this and see what you get using algebra.

 

 

Answer 3

That is my answer, as well, Alex.