Find the Inverse f(x)=3/(2x-5)

Problem

ƒ(x)=3/(2*x−5)

Solution

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

y=3/(2*x−5)

2. Swap the variables x and y to represent the inverse relationship.

x=3/(2*y−5)

3. Multiply both sides by the denominator 2*y−5 to begin isolating y

x*(2*y−5)=3

4. Distribute x into the binomial.

2*x*y−5*x=3

5. Isolate the term containing y by adding 5*x to both sides.

2*x*y=5*x+3

6. Divide both sides by 2*x to solve for y

y=(5*x+3)/(2*x)

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

ƒ(x)(−1)=(5*x+3)/(2*x)

Final Answer

ƒ(x)(−1)=(5*x+3)/(2*x)

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