Answer
$$ - \frac{1}{8}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}f\left( x \right) = {x^2} - 2x - 3;\,\,\,\,\,\left( {12, - 3} \right) \cr
& {\text{Calculate }}f'\left( { - 3} \right) \cr
& f'\left( x \right) = 2x - 2 \cr
& f'\left( { - 3} \right) = 2\left( { - 3} \right) - 2 \cr
& 3f'\left( { - 3} \right) = - 8 \cr
& {\text{Find the derivative of the inverse function}}{\text{, using the THEOREM 3}}{\text{.23}} \cr
& \left( {{f^{ - 1}}} \right)'\left( {{y_0}} \right) = \frac{1}{{f'\left( {{x_0}} \right)}},\,\,\,\,{\text{Where }}{y_0} = f\left( {{x_0}} \right) \cr
& {\text{Then}}{\text{,}} \cr
& \left( {{f^{ - 1}}} \right)'\left( {12} \right) = \frac{1}{{ - 8}} \cr
& \left( {{f^{ - 1}}} \right)'\left( {12} \right) = - \frac{1}{8} \cr} $$
