Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
MHT CET20239 May 2023Evening ShiftMathematicsDifferentiationActual

If g is the inverse of f and f^ (x)= 1 1+x^3 , then g^ (x) is

Options

  1. A1 1+( g (x))^3
  2. B1+(g(x))^3
  3. Cg(x) 1+(g(x))^3
  4. D(g(x))^3 1+(g(x))^3

Correct answer

B. 1+(g(x))^3

Step-by-step solution

array ll & g (x) is inverse of function f (x) & i.e., g (x)= f ⁻¹(x) & f ( g (x))=x & differentiating w.r.t. x , we get & f ^ ( g (x)) g ^ (x)=1 & g ^ (x)= 1 f ^ ( g (x)) ... (i) array Now, f ^ (x)= 1 1+x^3 ... [Given] f ^ ( g (x))= 1 1+( g (x))^3 ... (ii) From (i) and (ii), we get aligned & g ^ (x)=1+( g (x))^3 & aligned

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