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 $f: [4, \infty) \to [1, \infty)$ be a function defined by $f(x) = 5^{x(x - 4)}$. Then $f^{-1}(x)$ is:

If $g$ is the inverse of $f$ and $f^{\prime}(x)=\frac{1}{1+x^3}$,then $g^{\prime}(x)$ is

If $f: R - \{\frac{3}{5}\} \rightarrow R - \{\frac{3}{5}\}$ is defined by $f(x) = \frac{3x+1}{5x-3}$,then which of the following is true?

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 $f(x) = \frac{2x - 1}{x + 5}, x \neq -5$ then $f^{-1}(x)$ is equal to