Question

NEED HELP ASAP!! Drag the tiles to the boxes to form the correct pairs. Not all tiles will be used. Match the function to its inverse. (See attachment below)

Answer 1

Explanation:

Answer 2

QUESTION 1

We have
`f(x)=(2x-1)/(x+2)`

Let
`y=(2x-1)/(x+2)`

Interchange x and y.

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

Solve for y.

First, cross multiply;

`x(y+2)=2y-1`

Expand now:

`xy+2x=2y-1`

Group the y-terms on the LHS

`xy-2y=-2x-1`

Factor y on the left hand side;

`(x-2)y=-2x-1`

Divide both sides by (x-2).

`y=(-2x-1)/(x-2)`

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

`\boxed{f(x)=(2x-1)/(x+2)\to f^(-1)(x)=(-2x-1)/(x-2)}`

QUESTION 2

Given:
`f(x)=(x-1)/(2x+1)`

Let
`y=(x-1)/(2x+1)`

Interchange x and y.

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

Solve for y

`x(2y+1)=y-1`

`2xy+x=y-1`

`2xy-y=-x-1`

`(2x-1)y=-x-1`

`y=(-x-1)/(2x-1)`

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

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

`\boxed{f(x)=(x-1)/(2x+1)\to f^(-1)(x)=(-x-1)/(2x-1)}`

QUESTION 3

Given :
`f(x)=(2x+1)/(2x-1)`

We let
`y=(2x+1)/(2x-1)`

Interchange x and y.

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

Solve for y;

`x(2y-1)=2y+1`

`2xy-x=2y+1`

`2xy-2y=x+1`

`(2x-2)y=x+1`

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

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

`\boxed{f(x)=(2x+1)/(2x-1)\to f^(-1)(x)=(x+1)/(2(x-1))}`