Question

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.

Match the function with its inverse.


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Answer 1

Explanation:

Answer 2

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

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

Part 3)
`f(x)=(2x+1)/(2x-1)` ----->
`f^(-1)(x)=(x+1)/(2(x-1))`

Part 4)
`f(x)=(x+2)/(-2x+1)` ---->
`f^(-1)(x)=(x-2)/(2x+1)`

Part 5)
`f(x)=(x+2)/(x-1)` ------->
`f^(-1)(x)=(x+2)/(x-1)`

Explanation:

Part 1) we have

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

Find the inverse

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

`x=(2y-1)/(y+2)\\ \\ xy+2x=2y-1\\ \\xy-2y=-2x-1\\ \\y[x-2]=-2x-1\\ \\y=(-2x-1)/(x-2)`

Let

`f^(-1)(x)=y`

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

Part 2) we have

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

Find the inverse

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

`x=(y-1)/(2y+1)\\ \\2xy+x=y-1\\ \\2xy-y=-x-1\\ \\y[2x-1]=-x-1\\ \\y=(-x-1)/(2x-1)`

Let

`f^(-1)(x)=y`

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

Part 3) we have

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

Find the inverse

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

`x=(2y+1)/(2y-1)\\ \\2xy-x=2y+1\\ \\2xy-2y=x+1\\ \\y[2x-2]=x+1\\ \\y=(x+1)/(2(x-1))`

Let

`f^(-1)(x)=y`

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

Part 4) we have

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

Find the inverse

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

`x=(y+2)/(-2y+1)\\ \\-2xy+x=y+2\\ \\-2xy-y=-x+2\\ \\y[-2x-1]=-x+2\\ \\y=(-x+2)/(-2x-1) \\ \\y=(x-2)/(2x+1)`

Let

`f^(-1)(x)=y`

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

Part 5) we have

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

Find the inverse

Let

y=f(x)

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

Exchange the variables x for y and t for x

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

Isolate the variable y

`x=(y+2)/(y-1)\\ \\xy-x=y+2\\ \\xy-y=x+2\\ \\y[x-1]=x+2\\ \\y=(x+2)/(x-1)`

Let

`f^(-1)(x)=y`

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