Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET202015 Oct 2020Evening ShiftMathematicsDifferentiationActual

If f and g are differentiable functions satisfying g ^ ( a )=2, ~g ( a )= b and fog = I , where is an identity function, then f ^ ( b ) is equal to

Options

  1. A1 2
  2. B3 2
  3. C2 3
  4. D2

Correct answer

A. 1 2

Step-by-step solution

Given g(a)=b, g^ (a)=2, f[g(x)]=x Now f^ [g(x)] g^ (x)=1 f^ (g(x))= 1 g^ (x) Put x=a , we get f^ [g(a)]= 1 g^ (a) f^ (b)= 1 2

Practice Differentiation on Quantrex Academy →

More from Differentiation

The domain of the derivative of the function f(x)= x 1+|x| is 2025If x= 2^ cosec ⁻¹ t and y= 2^ ⁻¹ t ,|t| 1 then d y d x = 2025If (a+ 2 b x)(a- 2 b y)=a^2-b^2 where a>b>0 , then at ( 4 , 4 ) , dy dx = 2025If x y - y x =0 , then d y d x = 2025If y = ( _ x x )^ x , then dy dx = 2025If f(x)=x^ Sec ⁻¹ x , then f^ (2)= 2025If y= x^4 3 x-5 (x^2-3 )(2 x-3) , then ( d y d x )_ x=2 = 2025If x^2+y^2+ y=4 , then the value of d^2 y d x^2 at x=-2 is 2025 Full Differentiation list All MHT CET PYQs