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BITSAT2015MathematicsDifferentiationActual

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

Options

  1. Acosec g ( x )
  2. Bg(x)
  3. C1 g(x)
  4. DNone of these

Correct answer

C. 1 g(x)

Step-by-step solution

Since, g is the inverse of function f . Therefore, g ( x )= f ⁻¹( x ) f [ g ( x )]= x fog ( x )= x , for all x Differentiate both side,w.r.tx d dx fog ( x ) = d dx ( x ), for all x f ^ [ g ( x )] g ^ ( x )=1, for all x g ( x ) g ^ ( x )=1, for all x (By defn of .f^ (x) ) g ^ ( x )= 1 g ( x )

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