Problem

Let

f, g

h

three function defined as follows:

f(x)=\frac{32}{4+x^2+x^4},\ g(x)=9+x^2

and

h(x)=-x^2-3x+k

. Identify which of the following statement(s) is (are) correct? (a) Number of integers in the range of

f(x)

is 8 (b) Number of integral values of

k

for which

h(f(x))>0

and

h(g(x))<0\ \forall x\in R

is 20 (c) Number of integral values of

k

for which

h(f(x))>0

and

h(g(x))<0\ \forall x\in R

is 19 (d) Maximum value of

g(f(x))

is 73