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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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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match-example-1

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Answer:

Explanation:

Drag the tiles to the boxes to form correct pairs. Not all tiles will be used. Match-example-1
User Zunino
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4 votes

Answer:

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)

User MDMalik
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