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AP EAMCET202316 May 2023Evening ShiftMathematicsFunctionsActual

If g(x) is the inverse of the function f(x) and f^ (x)= 1 h(x) , then g^ (x)=

Options

  1. Ah(g(x))
  2. Bg ( h ( x ))
  3. Ch^ (f(x))
  4. Df(h(x))

Correct answer

A. h(g(x))

Step-by-step solution

Given g(x) is inverse of the function f(x) & f^ (x)= 1 ~h ( x ) Now, g(x)=f⁻¹(x) f(g(x))=x Differentiating w.r. to x . aligned & f ^ ( g ( x )) g ^ ( x )=1 g ^ ( x )= 1 f ^ ( g ( x )) & = 1 (1 / h ( g ( x ))) = h ( g ( x )) aligned

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