Find the Inverse f(x)=5/(x-2)

Problem

ƒ(x)=5/(x−2)

Solution

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

y=5/(x−2)

2. Swap the variables x and y to begin finding the inverse relationship.

x=5/(y−2)

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

x*(y−2)=5

4. Divide both sides by x to isolate the term containing y

y−2=5/x

5. Add 2 to both sides to solve for y

y=5/x+2

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

ƒ(x)(−1)=5/x+2

Final Answer

ƒ(x)(−1)=5/x+2

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