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

Problem

ƒ(x)=x/(x+2)

Solution

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

y=x/(x+2)

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

x=y/(y+2)

3. Multiply both sides by the denominator (y+2) to clear the fraction.

x*(y+2)=y

4. Distribute x into the parentheses.

x*y+2*x=y

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

2*x=y−x*y

6. Factor out y from the right side of the equation.

2*x=y*(1−x)

7. Divide both sides by (1−x) to solve for y

y=(2*x)/(1−x)

8. Replace y with ƒ(x)^(−1) to write the final inverse function.

ƒ(x)^(−1)=(2*x)/(1−x)

Final Answer

ƒ(x)^(−1)=(2*x)/(1−x)

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