`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

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

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

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

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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____

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 (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) (a) g(x)=sqrt(1+x^2)

If f(x)=(a x^2+b)^3, then find the function g such that f(g(x))=g(f(x))dot