Find the Inverse f(x)=-7/2x-3

Problem

ƒ(x)=−7/2*x−3

Solution

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

y=−7/2*x−3

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

x=−7/2*y−3

3. Isolate the term containing y by adding 3 to both sides of the equation.

x+3=−7/2*y

4. Multiply both sides by −2/7 to solve for y

−2/7*(x+3)=y

5. Distribute the fraction to simplify the expression for the inverse function.

y=−2/7*x−6/7

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

ƒ(x)(−1)=−2/7*x−6/7

Final Answer

ƒ(x)(−1)=−2/7*x−6/7

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