The inverse of the function $f(x) = \frac{{{e^x} – {e^{ – x}}}}{{{e^x} + {e^{ – x}}}} + 2$ is given by

If $f$ be the greatest integer function and $g$ be the modulus function, then $(gof)\left( { – \frac{5}{3}} \right) – (fog)\left( { – \frac{5}{3}} \right) = $

If the function $f:[1,\;\infty ) \to [1,\;\infty )$ is defined by $f(x) = {2^{x(x – 1)}},$ then ${f^{ – 1}} (x)$ is

Which of the following function is invertible

State with reason whether following functions have inverse $f: \{1,2,3,4\}\rightarrow\{10\}$ with $f =\{(1,10),(2,10),(3,10),(4,10)\}$