If $f\left(x\right)=23-2^{-x^2+2x+3}\mathrm{\forall }x\in R$ and $g\left(x\right)=\left[\frac{f\left(x\right)}{\mu }\right]$ where [K] denotes greatest integer function
and $\mu \in N$, then the sum of all values of$\mu$  for which g(x) is discontinuous for atleast are
real value of x

$\begin{array}{l}f\left(x\right)=23-2^{-x^2+2x+3}\\ f\left(x\right)=23-2^{4-(x^2-2x+!)}\\ f\left(x\right)=23-\frac{16}{2^{(x-1{)}^2}}\\ f\left(x\right)\in [7,23]\\ \mu \ge 23\Rightarrow 0<\frac{f\left(x\right)}{\mu }<1\\ \left[\frac{f\left(x\right)}{\mu }\right]=0\end{array}$

When $1\le \mu <23$ then $\frac{f\left(x\right)}{\mu }$be comes integer at same values of x and g(x) will be
discontinuous at these values of x.

Sum of all values of $\mu$.

$\begin{array}{l}=1+2+3+\dots +22\\ =\frac{22\times 23}{2}=253\end{array}$