Let $$ f(x)=\frac{x+3}{x+8} $$ $$ f^{-1}(-1)=\square $$

Question

UpStudy AI · Accepted Answer

1. We have the function 
   $$
   f(x)=\frac{x+3}{x+8}.
   $$

2. To find $$ f^{-1}(-1) $$, we need to solve
   $$
   \frac{x+3}{x+8} = -1.
   $$

3. Multiply both sides by $$ x+8 $$ (assuming $$ x \neq -8 $$):
   $$
   x+3 = -1 \cdot (x+8) = -x-8.
   $$

4. Add $$ x $$ to both sides:
   $$
   x + x + 3 = -8,
   $$
   which simplifies to
   $$
   2x + 3 = -8.
   $$

5. Subtract 3 from both sides:
   $$
   2x = -11.
   $$

6. Divide both sides by 2:
   $$
   x = -\frac{11}{2}.
   $$

7. Therefore, 
   $$
   f^{-1}(-1) = -\frac{11}{2}.
   $$
$$ f^{-1}(-1) = -\frac{11}{2} $$

Let \( f(x)=\frac{x+3}{x+8} \) \( f^{-1}(-1)=\square \)