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

If $f:[1, \infty) \rightarrow [1, \infty)$ is defined by $f(x) = \frac{1+\sqrt{1+4 \log_2 x}}{2}$, then $f^{-1}(3) =$

Let $f : R \rightarrow R$ be defined by $f(x) = x^3 - 3x^2 + 3x - 2$. Then $f^{-1}(x)$ is given by:

Let $f: R \rightarrow R$ be defined by $f(x) = 2x + 6$,which is a bijective mapping. Then $f^{-1}(x)$ is given by:

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

If $f(x) = x^{11} + \sin^3(35x) + 111x$,then the value of $f^{-1}(\sin \frac{\pi}{5}) + f^{-1}(\sin \frac{6\pi}{5}) + f^{-1}(\sin \frac{\pi}{7}) + f^{-1}(\sin \frac{8\pi}{7})$ is equal to