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

If $f:[1, \infty) \rightarrow [0, \infty)$ is given by $f(x) = x - \frac{1}{x}$,then $f^{-1}(x) =$

If a function $f:(-1,1) \rightarrow B(\subseteq R)$ is defined as $f(x)=x+x^2+x^3+\ldots \infty$,then in order to have the inverse function of $f$,$B$ is equal to

Let $f(x) = x^5 + 2e^{x/4}$ for all $x \in \mathbb{R}$. Consider a function $g(x)$ such that $(g \circ f)(x) = x$ for all $x \in \mathbb{R}$. Then the value of $8g'(2)$ is:

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 $f$?

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