Question

Sorry if this is too much but I'm desperate right now.

Answer 1

`f(x)=(2x-1)/(x+2)\\ \\f^(-1)(x)=(-2x-1)/(x-2)`

`f(x)=(x-1)/(2x+1)\\ \\f^(-1)(x)=(-x-1)/(2x-1)`

`f(x)=(x+2)/(-2x+1)\\ \\f^(-1)(x)=(2-x)/(-2x-1)=(x-2)/(2x+1)`

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

`f(x)=(x+2)/(x-1)\\ \\f^(-1)(x)=(x+2)/(x-1)` - extra

Explanation:

1.

`f(x)=y=(2x-1)/(x+2)\\ \\y(x+2)=2x-1\\ \\yx+2y=2x-1\\ \\yx-2x=-1-2y\\ \\x(y-2)=-1-2y\\ \\x=(-1-2y)/(y-2)\\ \\y=f^(-1)(x)=(-2x-1)/(x-2)`

2.

`f(x)=y=(x-1)/(2x+1)\\ \\y(2x+1)=x-1\\ \\2xy+y=x-1\\ \\2xy-x=-1-y\\ \\x(2y-1)=-1-y\\ \\x=(-1-y)/(2y-1)\\ \\y=f^(-1)(x)=(-x-1)/(2x-1)`

3.

`f(x)=y=(x+2)/(-2x+1)\\ \\y(-2x+1)=x+2\\ \\-2xy+y=x+2\\ \\-2xy-x=2-y\\ \\x(-2y-1)=2-y\\ \\x=(2-y)/(-2y-1)\\ \\y=f^(-1)(x)=(2-x)/(-2x-1)=(x-2)/(2x+1)`

4.

`f(x)=y=(2x+1)/(2x-1)\\ \\y(2x-1)=2x+1\\ \\2xy-y=2x+1\\ \\2xy-2x=1+y\\ \\x(2y-2)=1+y\\ \\x=(1+y)/(2y-2)\\ \\y=f^(-1)(x)=(1+x)/(2(x-1))`

5.

`f(x)=y=(x+2)/(x-1)\\ \\y(x-1)=x+2\\ \\xy-y=x+2\\ \\xy-x=2+y\\ \\x(y-1)=2+y\\ \\x=(2+y)/(y-1)\\ \\y=f^(-1)(x)=(x+2)/(x-1)`