If `f(x) and g(x)` are mirror image of each other through `y = x` and such that `f(x) = e^x + x` then the value of `g'(1)` is

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

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

If the function f(x) = 2+x^2-e^x and g(x) = f^(-1)(x) , then the value of |g^'(1)|/4 equals

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

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

Let f:(-0, 2] -> [6,oo) be defined as f(x) = 4x^2 – 16x + 22 and g(x) is a function such that graphs of f(x) and g(x) are mirror image of each other with respect to line x-y=0, then g(10) is equal to

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