Question
Let \( f(x)=\frac{x+3}{x+8} \) \( f^{-1}(-1)=\square \)
Ask by Campos Ford. in the United States
Mar 15,2025
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Answer
\( f^{-1}(-1) = -\frac{11}{2} \)
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To find \( f^{-1}(-1) \), we first set \( f(x) \) equal to \(-1\): \[ \frac{x + 3}{x + 8} = -1 \] Now, multiply both sides by \( x + 8 \) to eliminate the fraction: \[ x + 3 = -1(x + 8) \] Simplifying this, we get: \[ x + 3 = -x - 8 \] Now, add \( x \) to both sides: \[ 2x + 3 = -8 \] Next, subtract \( 3 \) from both sides: \[ 2x = -11 \] Finally, divide by 2: \[ x = -\frac{11}{2} \] Thus, \( f^{-1}(-1) = -\frac{11}{2} \).