Find the Inverse f(x)=(2-x)/(3+x)

Problem

ƒ(x)=(2−x)/(3+x)

Solution

1. Replace ƒ(x) with y to make the equation easier to manipulate.

y=(2−x)/(3+x)

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

x=(2−y)/(3+y)

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

x*(3+y)=2−y

4. Distribute x into the parentheses.

3*x+x*y=2−y

5. Rearrange the equation to group all terms containing y on one side and all other terms on the opposite side.

x*y+y=2−3*x

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

y*(x+1)=2−3*x

7. Isolate y by dividing both sides by (x+1)

y=(2−3*x)/(x+1)

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

ƒ(x)(−1)=(2−3*x)/(x+1)

Final Answer

ƒ(x)(−1)=(2−3*x)/(x+1)

Want more problems? Check here!