Find the Inverse f(x)=x/(x+4)

Problem

ƒ(x)=x/(x+4)

Solution

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

y=x/(x+4)

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

x=y/(y+4)

3. Multiply both sides by the denominator (y+4) to clear the fraction.

x*(y+4)=y

4. Distribute x into the parentheses.

x*y+4*x=y

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

4*x=y−x*y

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

4*x=y*(1−x)

7. Solve for y by dividing both sides by (1−x)

y=(4*x)/(1−x)

8. Replace y with the inverse function notation ƒ(x)^(−1)

ƒ(x)^(−1)=(4*x)/(1−x)

Final Answer

ƒ(x)^(−1)=(4*x)/(1−x)

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