If ${e^x} = y + \sqrt {1 + {y^2}} $,then $y =$

Let $f: N \rightarrow Y$ be a function defined as $f(x) = 4x + 3$,where $Y = \{y \in N : y = 4x + 3\}$ for some $\{x \in N\}$. Show that $f$ is invertible. Find the inverse.

Let $f: X \rightarrow Y$ be an invertible function. Show that the inverse of $f^{-1}$ is $f$,i.e.,$\left(f^{-1}\right)^{-1}=f$.

If $f(x) = \int\limits_0^x {\frac{1}{{\sqrt {1 + {t^3}} }}\,} dt$ and $h(x)$ is the inverse of $f(x)$,then the value of $\frac{{h''(x)}}{{{h^2}(x)}}$ is

$f: R \rightarrow R, f(x) = 3x + 2$ and $g: R \rightarrow R, g(x) = 6x + 5$. Find the value of $(g \circ f^{-1})(10)$.

Let $f:(2, 3) \to (0, 1)$ be defined by $f(x) = x - [x]$. Then ${f^{ - 1}}(x)$ equals: