Home
Class 12
MATHS
f is a strictly monotonic differentiable...

`f` is a strictly monotonic differentiable function with `f^(prime)(x)=1/(sqrt(1+x^3))dot` If `g` is the inverse of `f,` then `g^(x)=` `(2x^2)/(2sqrt(1+x^3))` b. `(2g^2(x))/(2sqrt(1+g^2(x)))` c. `3/2g^2(x)` d. `(x^2)/(sqrt(1+x^3))`

A

`(3x^(2))/(2sqrt(1+x^(3)))`

B

`(3g^(2)(x))/(2sqrt(1+g^(2)(x)))`

C

`(3)/(2)g^(2)(x)`

D

`(x^(2))/(sqrt(1+x^(3)))`

Text Solution

Verified by Experts

The correct Answer is:
C
g is inverse of f
`therefore" "fog(x)=x`
`therefore" "f'(g(x)).g'(x)=1`
`therefore" "g'(x)=(1)/(f'(g(x)))" (1)"`
`=sqrt(1+g^(3)(x))`
`therefore" "g''(x)=(3g^(2)(x).g'(x))/(2sqrt(1+g^(3)(x)))`
`=(3g^(2)(x))/(2)" (using (1))"`
Promotional Banner

Topper's Solved these Questions

  • METHODS OF DIFFERENTIATION

    CENGAGE|Exercise Multiple Correct Answer Type|7 Videos

  • MATRICES

    CENGAGE|Exercise Multiple Correct Answer|7 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|13 Videos

Similar Questions

Explore conceptually related problems

f is a strictly monotonic differentiable function with f^(prime)(x)=1/(sqrt(1+x^3))dot If g is the inverse of f, then g^(x)= a. (2x^2)/(2sqrt(1+x^3)) b. (2g^2(x))/(2sqrt(1+g^2(x))) c. 3/2g^2(x) d. (x^2)/(sqrt(1+x^3))

Let f(x)=int_2^x (dt)/sqrt(1+t^4) and g be the inverse of f . Then, the value of g'(x) is

If x in[-1,(-1)/(sqrt(2))] , then the inverse of the function f(x)=sin^(-1)(2x sqrt(1-x^(2))) is given by

If g is the inverse of a function f and f^'(x)=1/(1+x^5) then g(x) is equal to (1) 1""+x^5 (2) 5x^4 (3) 1/(1+{g(x)}^5) (4) 1+{g(x)}^5

Find the domain of the following functions: f(x)=sqrt((x-2)/(x+2))+sqrt((1-x)/(1+x))

consider the functions f(x) = sqrt(x-2) , g(x) = ( x+1)/( x^2 -2x +1) domain of g

consider the functions f(x) = sqrt(x-2) , g(x) = ( x+1)/( x^2 -2x +1) domain of f

If f(x)=x+tanxa n df is the inverse of g, then g^(prime)(x) equals (a) 1/(1+[g(x)-x]^2) (b) 1/(2-[g(x)-x]^2) (c) 1/(2+[g(x)-x]^2) (d) none of these

If f(x)=3sqrt(1−x^2)​+3sqrt(1−x^2)​, then f(x) is

Let f(x)=int_0^x(dt)/(sqrt(1+t^3))a n dg(x) be the inverse of f(x) . Then the value of 4(g^(primeprime)(x))/((g(x))^2)i s____