Question

Find the inverse of f(x)=(x+1)(x+2). Show your work how to get the answer.

Answer 1

Answer:

$f^{-1}(x)=\frac{1-2x}{x-1}$

Step-by-step explanation:

1. replace f(x) with x, and x with y:  $f(x)=\frac{x+1}{x+2} == > x=\frac{y+1}{y+2}$

2. Solve for y:

   $x=\frac{y+1}{y+2}$

   $x(y+2)=y+1$

   $xy+2x=y+1$

   $xy-y=1-2x$

   $y(x-1)=1-2x$

   $y=\frac{1-2x}{x-1}$

3. Replace y with f⁻¹(x)