If the function `f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x)`, then the value of `g'(1)` is

If the functions f(x)=x^(5)+e^(x//3) " and " g(x)=f^(-1)(x) , the value of g'(1) is ………… .

Let f(x)=x^(2)-2x and g(x)=f(f(x)-1)+f(5-f(x)), then

f(x)= 3x^(2)-1 and g(x)= 3 + x . If f= g then the value of x is…….

f(x)= x^(2)-3x + 4 If f(x)= f(2x+1) find the value of x .

"If "f(x)=(x-1)^(4)(x-2)^(3)(x-3)^(2)(x-4), then the value of f'''(1)+f''(2)+f'(3)+f'(4) equals

If real function f(x) =(x+1)^(2) and g(x) =x^(2) +1 then (fog) (-3) = ..........

If x=2 is a real root of cubic equation f (x) = 3x^(3)+bx^(2)+bx+3=0 . Then the value of lim_(xrarr(1)/(2)) (e^(f(x)-1)/(2x-1))

For the function f(x)= x + (1)/(x), x in [1, 3] the value of c for mean value theorem is

Let f(x) be a continuous function defined for 1 <= x <= 3. If f(x) takes rational values for all x and f(2)=10 then the value of f(1.5) is :

If alpha, beta (where alpha lt beta ) are the points of discontinuity of the function g(x) = f(f(f(x))), where f(x) = (1)/(1-x) . Then, The points of discontinuity of g(x) is