Find the Inverse f(x)=(4x-1)/(2x+3)

Problem

ƒ(x)=(4*x−1)/(2*x+3)

Solution

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

y=(4*x−1)/(2*x+3)

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

x=(4*y−1)/(2*y+3)

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

x*(2*y+3)=4*y−1

4. Distribute x into the terms on the left side of the equation.

2*x*y+3*x=4*y−1

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

2*x*y−4*y=−3*x−1

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

y*(2*x−4)=−3*x−1

7. Isolate y by dividing both sides by the expression (2*x−4)

y=(−3*x−1)/(2*x−4)

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

y=(3*x+1)/(4−2*x)

Final Answer

ƒ(x)(−1)=(3*x+1)/(4−2*x)

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