Exercise 6 Page 267

Before we can find the inverse of the given function, we need to replace f(x) with y. f(x)=2/3x+6 ⇔ y=2/3x+6 Now, to algebraically determine the inverse of the given equation, we exchange x and y and solve for y. Given Equation & Inverse Equation y=2/3 x+6 & x=2/3 y+6 The result of isolating y in the new equation will be the inverse of the given function.

x=2/3y+6

▼

Solve for y

SubEqn

LHS-6=RHS-6

x-6=2/3y

MultEqn

LHS * 3=RHS* 3

3x-18=2y

DivEqn

.LHS /2.=.RHS /2.

3x-18/2=y

WriteDiffFrac

Write as a difference of fractions

3x/2-18/2=y

MovePartNumRight

a* b/c=a/c* b

3/2x-18/2=y

CalcQuot

Calculate quotient

3/2x-9=y

RearrangeEqn

Rearrange equation

y= 3/2x-9

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)=3/2x-9