Exercise 22 Page 268

To find the inverse of the given equation, we exchange x and y and solve for y. Given Equation & Inverse Equation 3 y-12 x=- 72 & 3 x-12 y=- 72The result of isolating y in the new equation will be the inverse of the given function.

3x-12y=- 72

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Solve for y

SubEqn

LHS-3x=RHS-3x

- 12y=- 3x-72

MultEqn

LHS * (- 1)=RHS* (- 1)

12y=3x+72

DivEqn

.LHS /12.=.RHS /12.

y=3x+72/12

WriteSumFrac

Write as a sum of fractions

y=3x/12+72/12

MovePartNumRight

a* b/c=a/c* b

y=3/12x+72/12

ReduceFrac

a/b=.a /3./.b /3.

y=1/4x+72/12

CalcQuot

Calculate quotient

y=1/4x+6

Finally, we write the inverse of the given equation in function notation by replacing y with f^(- 1)(x) in our new equation. f^(- 1)(x)=1/4x+6