Find the Inverse f(x)=(8x)/(3x-7)

Problem

ƒ(x)=(8*x)/(3*x−7)

Solution

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

y=(8*x)/(3*x−7)

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

x=(8*y)/(3*y−7)

3. Multiply both sides by the denominator (3*y−7) to clear the fraction.

x*(3*y−7)=8*y

4. Distribute x into the parentheses.

3*x*y−7*x=8*y

5. Rearrange the equation to group all terms containing y on one side and terms without y on the other.

3*x*y−8*y=7*x

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

y*(3*x−8)=7*x

7. Isolate y by dividing both sides by (3*x−8)

y=(7*x)/(3*x−8)

8. Rewrite the result using inverse function notation ƒ(x)(−1)

ƒ(x)(−1)=(7*x)/(3*x−8)

Final Answer

ƒ(x)(−1)=(7*x)/(3*x−8)

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