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Let f: RvecR be a one-one onto different...

Let `f: RvecR` be a one-one onto differentiable function, such that `f(2)=1a n df^(prime)(2)=3.` The find the value of `((d/(dx)(f^(-1)(x))))_(x=1)`

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To solve the problem, we need to find the derivative of the inverse function \( f^{-1}(x) \) at the point \( x = 1 \). We are given that \( f(2) = 1 \) and \( f'(2) = 3 \). ### Step-by-step Solution: 1. **Understand the relationship between the function and its inverse**: Since \( f \) is a one-to-one and onto function, it has an inverse \( f^{-1} \). By the property of derivatives of inverse functions, we have: \[ \frac{d}{dx}(f^{-1}(x)) = \frac{1}{f'(f^{-1}(x))} ...
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