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AP EAMCET · Maths · Functions

If \(g(x)\) is the inverse of the function \(f(x)\) and \(f^{\prime}(x)=\frac{1}{h(x)}\), then \(g^{\prime}(x)=\)

  1. A \(h(g(x))\)
  2. B \(\mathrm{g}(\mathrm{h}(\mathrm{x}))\)
  3. C \(h^{\prime}(f(x))\)
  4. D \(f(h(x))\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(h(g(x))\)

Step-by-step Solution

Detailed explanation

Given \(g(x)\) is inverse of the function \(f(x) \& f^{\prime}(x)\) \(=\frac{1}{\mathrm{~h}(\mathrm{x})}\) Now, \(g(x)=f^{-1}(x) \Rightarrow f(g(x))=x\) Differentiating w.r. to \(x\).…