Answer is: option2
\( \frac{-1}{2} \)Solution:
Since \( h(x) = g^{-1}(x) \), the derivative of the inverse function \( h'(x) \) is given by the formula: \[ h'(x) = \frac{1}{g'(h(x))} \] We are asked to find \( h'(6) \). From the given information, \( g(3) = 6 \), which means \( h(6) = 3 \). Now we can compute \( h'(6) \) as follows: \[ h'(6) = \frac{1}{g'(h(6))} = \frac{1}{g'(3)} \] Since \( g'(3) = -2 \), we have: \[ h'(6) = \frac{1}{-2} = -\frac{1}{2} \]
Final Answer:
The correct answer is B) \( \frac{1}{-2} \).