Find the Inverse f(x)=(2x+1)/x

Problem

ƒ(x)=(2*x+1)/x

Solution

1. Replace ƒ(x) with y to set up the equation for the inverse.

y=(2*x+1)/x

2. Swap the variables x and y to begin solving for the inverse function.

x=(2*y+1)/y

3. Multiply both sides by y to clear the fraction.

x*y=2*y+1

4. Isolate the terms containing y on one side of the equation by subtracting 2*y from both sides.

x*y−2*y=1

5. Factor out the common variable y from the left side.

y*(x−2)=1

6. Solve for y by dividing both sides by (x−2)

y=1/(x−2)

7. Replace y with the inverse notation ƒ(x)(−1)

ƒ(x)(−1)=1/(x−2)

Final Answer

ƒ(x)(−1)=1/(x−2)

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