If `g` is the inverse of `fandf(x) = x^(2)+3x-3,(xgt0).` then `g'(1)` equals

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 f:R to R, g: R to R be two functions given by f(x)=2x-3,g(x)=x^(3)+5 . Then (fog)^(-1) is equal to

Find the values of x for which the functions f(x)= 3x^(2)-1 and g(x)= 3 + x are equal

If f and g are two real valued functions defined as f(x)= 2x+1 and g(x)= x^(2)+1 , then find (f)/(g) .

Evaluation of definite integrals by subsitiution and properties of its : F(x)=int_(x^(2))^(x^(3))logt.dt(xgt0) then F'(x)= ………….

f(x+y) = f(x) + f(y), "for " AA x and y and f(x)= (2x^(2) + 3x) g(x) . For AA x . If g(x) is a continuous function and g(0)= 3 then f'(x) = ……….

Let A = {-1,0,1,2}, B = {-4,-2,0,2} and f , g : A rarr B be functions defined f(x) = x^(2)-x, x inR and g(x) = 2 |x-(1)/2|-1,x inR . Are f and g equal ? Justify your answer. (Hint : One may note that two functions f : A rarr B and g : A rarr B such that f (a) = g(a) A a inA, are called equal functions).

If f and g are two real valued functions defined as f(x)= 2x+1 and g(x)= x^(2)+1 , then find f+g