what is the f inverse of x of f(x) = 2-3x/x+1 ?

Question

f(x) = 2-3x / x+1

 

What is the f ^-1(x)? How to prove it through Composite Function? 

Answer 1

I assume you mean f(x) = (2 -3x)/(x + 1)

 

Interchange the roles of x and y

 

x = (2 - 3y)/(y + 1)

 

xy + x = 2 - 3y

xy + 3y = 2 - x

y(x + 3) = 2 - x

y = (2-x)/(x + 3) = f^-1(x)

f(f^-1(x) = x so substitute the expression for f^-1(x) into the expression for f(x) and see if you get back x!