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

Let $f: X \rightarrow Y$ be an invertible function. Show that $f$ has a unique inverse.
(Hint: Suppose $g_{1}$ and $g_{2}$ are two inverses of $f$. Then for all $y \in Y$,$f \circ g_{1}(y) = I_{Y}(y) = f \circ g_{2}(y)$. Use the one-one property of $f$.)

If $g(x)$ is the inverse function of $f(x)$ and $f^{\prime}(x) = \frac{1}{1+x^4}$,then $g^{\prime}(x)$ is

If $y = f(x) = \frac{x + 2}{x - 1}$,then $x = $

If $f: R \rightarrow R$ is defined by $f(x)=|x|$,then

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