Question

homework assignment 1.7: inverse functions
score: 12.5/15 answered: 13/15
question 14
let
$f(x) = \frac{x + 3}{x + 6}$
$f^{-1}(-4) = $
question help: video written example

Explanation:

Step1: Recall inverse function definition

To find \( f^{-1}(-4) \), we use the property that if \( f(a) = b \), then \( f^{-1}(b) = a \). So we set \( f(x)=-4 \) and solve for \( x \).
\[
\frac{x + 3}{x + 6}=-4
\]

Step2: Solve the equation for \( x \)

Multiply both sides by \( x + 6 \) (assuming \( x
eq - 6\)):
\[
x + 3=-4(x + 6)
\]
Expand the right - hand side:
\[
x + 3=-4x-24
\]
Add \( 4x \) to both sides:
\[
5x + 3=-24
\]
Subtract 3 from both sides:
\[
5x=-27
\]
Divide both sides by 5:
\[
x =-\frac{27}{5}=-5.4
\]

Answer:

\(-\frac{27}{5}\) (or - 5.4)