Let f, g and h be three functions defined as follows:  $f\left(x\right)=\frac{32}{4+x^2+x^4},g\left(x\right)=9+x^2,$  and  $h\left(x\right)=-x^2-3x+k$. Identify which of the following statement(s) is(are) correct?

number of integers in the range of f(x) is 8

number of integral values of K for which $h\left(f\left(x\right)\right)>0$ and  $h\left(g\left(x\right)\right)<0\forall x\in R$ is 20

number of integral values of K for which  $h\left(f\left(x\right)\right)>0$  and  $h\left(g\left(x\right)\right)<0\forall x\in R$ is 19

maximum value of  $g\left(f\left(x\right)\right)$ is 73