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

Problem

ƒ(x)=(x−3)/(x+2)

Solution

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

y=(x−3)/(x+2)

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

x=(y−3)/(y+2)

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

x*(y+2)=y−3

4. Distribute x into the terms inside the parentheses.

x*y+2*x=y−3

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*x−3

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

y*(x−1)=−2*x−3

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

y=(−2*x−3)/(x−1)

8. Simplify the expression by multiplying the numerator and denominator by −1 to remove leading negatives.

y=(2*x+3)/(1−x)

Final Answer

ƒ(x)(−1)=(2*x+3)/(1−x)

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