Exercise 17 Page 268

Before we can find the inverse of the given function, we need to replace f(x) with y. f(x)=12-6x ⇔ y=12-6x Now, to algebraically determine the inverse of the given equation, we exchange x and y and solve for y. Given Equation & Inverse Equation y=12-6 x & x=12-6 y The result of isolating y in the new equation will be the inverse of the given function.

x=12-6y

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Solve for y

SubEqn

LHS-12=RHS-12

x-12=- 6y

MultEqn

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

- x+12=6y

DivEqn

.LHS /6.=.RHS /6.

- x+12/6=y

WriteSumFrac

Write as a sum of fractions

- x/6+12/6=y

MoveNegNumToFrac

Put minus sign in front of fraction

-x/6+12/6=y

MoveNumRight

a/b=1/b* a

-1/6x+12/6=y

CalcQuot

Calculate quotient

-1/6x+2=y

RearrangeEqn

Rearrange equation

y= -1/6x+2

Finally, we write the inverse of the given function in function notation by replacing y with f^(- 1)(x) in our new equation. f^(- 1)(x)=-1/6x+2