If $y = f(x) = \frac{ax + b}{cx - a}$,then $x$ is equal to

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

Let $Y = \{n^{2} : n \in N\} \subset N$. Consider $f: N \rightarrow Y$ as $f(n) = n^{2}$. Show that $f$ is invertible. Find the inverse of $f$.

Let $f(x) = \int\limits_2^x \frac{dt}{\sqrt{1 + t^4}}$ and $g$ be the inverse of $f$. Then the value of $g'(0)$ is

The relation $R$ on the set of natural numbers is defined by $R = \{(a, b) : a = 2b\}$. Then ${R^{-1}}$ is:

Let $f$ and $g$ be two differentiable functions satisfying $g^{\prime}(5)=\frac{3}{4}$, $g(5)=6$ and $g=f^{-1}$. Then $f^{\prime}(6)$ is equal to