If the function `f(x)=4e^((1-x)/2)+1+x+(x^2)/2+x^2/3 and g(x) =f^(-1)(x)` then the reciprocal of `g((-7)/6)` is .......

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

f(x) = x^(2)+xg'(1) +g''(2) and g(x) =f(1)x^2+xf'(x)+f''(x) The value of g(0) is

f(x)=(1)/(2)-tan((pi x)/(2)), -1 lt x lt 1 and g(x)=sqrt(3+4x-4x^(2)) then domain of (f+g) is

f(x) = x^(2)+xg'(1) +g''(2) and g(x) =f(1)x^2+xf'(x)+f''(x) The value of f(3) is

If f(x)=1+1//x, g(x)=sqrt(1-x^(2)) , then the domain of f(x)-g(x) is

The function f(x) =(e^(1//x^(2))/(e^(1//x^(2))-1)" for "x ne 0,f(0)=1" at x =0 is"

If f(g(x)) = x and g(f(x)) = x then g(x) is the inverse of f(x) . (g'(x))f'(x) = 1 implies g'(f(x))=1/(f'(x)) Let us consider a real value bijective function g(x) sun that g'(x) = sin^2 (x+pi/4) +2 cos (x -pi/4) and g(pi/4) =3 then value of (g^(-1))(3) is

If f and g are real functions defined by f(x) =2x-1 and g(x) =x^(2) , then prove that (3f-2g)(1)=1