Let \( f(x)=\frac{x+1}{x+8} \) \( f^{-1}(-4)=\square \)

To find the value of \( f^{-1}(-4) \), we need to find the value of \( x \) for which \( f(x) = -4 \). Given the function \( f(x) = \frac{x+1}{x+8} \), we set it equal to -4 and solve for \( x \): \[ \frac{x+1}{x+8} = -4 \] To solve for \( x \), we can cross-multiply: \[ x + 1 = -4(x + 8) \] Now, distribute the -4 on the right side: \[ x + 1 = -4x - 32 \] Next, we want to get all the \( x \) terms on one side and the constants on the other side. We can do this by adding \( 4x \) to both sides and subtracting 1 from both sides: \[ x + 4x = -32 - 1 \] This simplifies to: \[ 5x = -33 \] Now, divide both sides by 5 to solve for \( x \): \[ x = \frac{-33}{5} \] So, \( f^{-1}(-4) = \frac{-33}{5} \).