If $g(x)$ is the inverse function of $f(x)$, where $f(x) = \frac{5x + 3}{4x - 1}$, then $g(1) = $

If $f(x) = 2 + |\sin^{-1} x|$ and $A = \{x \in R : f^{-1}(x) \text{ exists} \}$,then $A = $

If $f(x) = \exp(2x^3 + 3x^2 + 6x)$ and $g(x)$ is the inverse function of $f(x)$,then the value of $g'(e^{11})$ is -

Show that $f:[-1,1] \rightarrow R$,given by $f(x)=\frac{x}{x+2}$ is one-one. Find the inverse of the function $f:[-1,1] \rightarrow \text{Range } f$.

The inverse of the function $y = \frac{10^x - 10^{-x}}{10^x + 10^{-x}} + 1$ is $x =$

If $f(x) = \frac{a^x - a^{-x}}{a^x + a^{-x}}$,where $a$ and $x$ satisfy the necessary conditions,then $f^{-1}(x) =$