Answer is: option2

Solution:

Step 1: Recall the inverse function derivative rule

If \( g \) is the inverse of \( f \), then the derivative of the inverse function at any point is given by the formula:

\[ (f^{-1})'(x) = \frac{1}{f'(f^{-1}(x))} \]

Step 2: Apply the given values

We are given that \( f(-3) = 2 \), so \( f^{-1}(2) = -3 \). Additionally, we know that \( f'(-3) = \frac{3}{4} \). Thus, from the formula for the derivative of the inverse function, we can substitute these values:

\[ (f^{-1})'(2) = \frac{1}{f'(-3)} = \frac{1}{\frac{3}{4}} = \frac{4}{3} \]

Final Answer:

The value of \( (f^{-1})'(2) \) is \( \frac{4}{3} \), so the correct answer is (B).