Exercise 19 Page 268

Before we can find the inverse of the given function, we need to replace f(x) with y. f(x)=- 16-4/3x ⇔ y=- 16-4/3x Now, to algebraically determine the inverse of the given equation, we exchange x and y and solve for y. Given Equation & Inverse Equation y=- 16-4/3 x & x=- 16-4/3 y The result of isolating y in the new equation will be the inverse of the given function.

x=- 16-4/3y

▼

Solve for y

AddEqn

LHS+16=RHS+16

x+16=-4/3y

MultEqn

LHS * (- 3)=RHS* (- 3)

- 3x-48=4y

DivEqn

.LHS /4.=.RHS /4.

- 3x-48/4=y

WriteDiffFrac

Write as a difference of fractions

- 3x/4-48/4=y

MoveNegNumToFrac

Put minus sign in front of fraction

-3x/4-48/4=y

MovePartNumRight

a* b/c=a/c* b

-3/4x-48/4=y

CalcQuot

Calculate quotient

-3/4x-12=y

RearrangeEqn

Rearrange equation

y= -3/4x-12

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)=-3/4x-12