`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))`

f(x)=1/abs(x), g(x)=sqrt(x^(-2))

Let g (x) be the inverse of f (x) =(2 ^(x+1)-2^(1-x))/(2 ^(x)+2 ^(-x)) then g (x) be :

Let f(x)=int_(0)^(x)(dt)/(sqrt(1+t^(3))) and g(x) be the inverse of f(x) . Then the value of 4 (g''(x))/(g(x)^(2)) is________.

Let g be the inverse function of f and f'(x)=(x^(10))/(1+x^(2)). If g(2)=a then g'(2) is equal to

Let g (x) be then inverse of f (x) such that f '(x) =(1)/(1+ x ^(5)), then (d^(2) (g (x)))/(dx ^(2)) is equal to:

Let g (x) be then inverse of f (x) such that f '(x) =(1)/(1+ x ^(5)), then (d^(2) (g (x)))/(dx ^(2)) is equal to:

Consider the function f(x)=tan^(-1){(3x-2)/(3+2x)}, AA x ge 0. If g(x) is the inverse function of f(x) , then the value of g'((pi)/(4)) is equal to

If differentiable function f(x) in inverse of g(x) then f^(g(x)) is equal to (g^(x))/((g^(prime)(x))^3) 2. 0 3. (g^(x))/((g^(prime)(x))^2) 4. 1

If f(x)=sqrt(x^(2)-1) and g(x)=(10)/(x+2) , then g(f(3)) =

Let g(x) be a function defined on [-1,1]dot If the area of the equilateral triangle with two of its vertices at (0,0) a n d (x ,g(x)) is (a) (sqrt(3))/4 , then the function g(x) is (b) g(x)=+-sqrt(1-x^2) (c) g(x)=sqrt(1-x^2) (d) g(x)=-sqrt(1-x^2) g(x)=sqrt(1+x^2)