If $g$ is the inverse of the function $f(x)$ and $g(x) = x + \tan x$,then $f^{\prime}(x) = $

$f: R \rightarrow R, f(x) = 3x + 2$ and $g: R \rightarrow R, g(x) = 6x + 5$. Find the value of $(g \circ f^{-1})(10)$.

If $f:[1, \infty) \rightarrow[5, \infty)$ is given by $f(x)=3x+\frac{2}{x}$, then $f^{-1}(x)=$

Let $A = \{1, 2, 3\}$ and $B = \{1, 3, 5\}$. $A$ relation $R: A \to B$ is defined by $R = \{(1, 3), (1, 5), (2, 1)\}$. Then ${R^{-1}}$ is defined by:

If the function $f(x)=x^3+e^{\frac{x}{2}}$ and $g(x)=f^{-1}(x)$,then the value of $g^{\prime}(1)$ is

Let $R$ denote the set of all real numbers. Let $f: R \rightarrow R$ and $g: R \rightarrow (0, 4)$ be functions defined by $f(x) = \log_e(x^2 + 2x + 4)$ and $g(x) = \frac{4}{1 + e^{-2x}}$. Define the composite function $h(x) = (f \circ g^{-1})(x)$,where $g^{-1}$ is the inverse of the function $g$. Then the value of the derivative of the composite function $h(x)$ at $x = 2$ is: