If $f: R \rightarrow R$ is given by $f(x)=7x+8$ and $f^{-1}(12)=\frac{k}{7}$,then the value of $k$ is

Let $f: R - \{-\frac{4}{3}\} \rightarrow R$ be a function defined as $f(x) = \frac{4x}{3x+4}$. The inverse of $f$ is the map $g: \text{Range } f \rightarrow R - \{-\frac{4}{3}\}$ given by

If $f(x)$ and $g(x)$ are inverse functions of each other and $f(x) = x + e^x$, then $g'(x) = ...$

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

If $f(x) = \frac{4x+3}{6x-4}, x \neq \frac{2}{3},$ show that $(f \circ f)(x) = x$ for all $x \neq \frac{2}{3}.$ What is the inverse of $f$?

State with reason whether the following function has an inverse: $h: \{2, 3, 4, 5\} \rightarrow \{7, 9, 11, 13\}$ with $h = \{(2, 7), (3, 9), (4, 11), (5, 13)\}$.