Answer is: option4
\( (h^{-1})'(5) = \frac{1}{7} \)Solution:
To solve this, we use the formula for the derivative of the inverse function: \[ (h^{-1})'(y) = \frac{1}{h'(h^{-1}(y))} \] We are asked to find \( (h^{-1})'(5) \). From the given information, we know that \( h(3) = 5 \), so \( h^{-1}(5) = 3 \). Using the formula for the inverse derivative, we have: \[ (h^{-1})'(5) = \frac{1}{h'(h^{-1}(5))} = \frac{1}{h'(3)} \] Since we are given that \( h'(3) = 7 \), we substitute this value into the formula: \[ (h^{-1})'(5) = \frac{1}{7} \] Thus, the correct statement is: \[ (h^{-1})'(5) = \frac{1}{7} \]
The correct answer is D) \( (h^{-1})'(5) = \frac{1}{7} \).