Exercise 63 Page 290

Before we can find the inverse of the given function, we need to replace

f (x)

with

y .

f (x) = - \frac{1}{3} x - 8 \Leftrightarrow y = - \frac{1}{3} x - 8

Now, to algebraically determine the inverse of the given equation, we exchange

x

and

y

and solve for

y .

\underline{Given Equation} y = - \frac{1}{3} x - 8 \underline{Inverse Equation} x = - \frac{1}{3} y - 8

The result of isolating

y

in the new equation will be the inverse of the given function.

x = - \frac{1}{3} y - 8

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Solve for

y

$LHS + 8 = RHS + 8$

x + 8 = - \frac{1}{3} y

$LHS \cdot (- 3) = RHS \cdot (- 3)$

- 3 (x + 8) = y

Distribute $- 3$

- 3 x - 24 = y

Rearrange equation

y = - 3 x - 24

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 x - 24