Question

Help anyone? dying ​

Answer 1

Answer:
`\bold{f^(-1)(x)=(2x-1)/(2+x)}`

Explanation:

Inverse is when you swap the x's and y's and then manipulate the equation to solve for y.

`y=(2x+1)/(2-x)\\\\\\\text{Swap the x's and y's:}\\x=(2y+1)/(2-y)\\\\\\\text{Multiply both sides by 2-y}:\\x(2-y)=2y+1\\\\\\\text{distribute x into 2-y}:\\2x-xy=2y+1\\\\\\\text{subtract 1 from both sides and add xy to both sides}:\\2x-1=2y+xy\\\\\\\text{factor out y from the right side}:\\2x-1=y(2+x)\\\\\\\text{divide 2+x from both sides}:\\(2x-1)/(2+x)=y\\\\\\\text{Therefore, the inverse }f^(-1)(x)=(2x-1)/(2+x)`