Let , , and be three functions defined as follows: , , and . Identify which of the…

MATHEMATICS · Multi correct · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Let

f

g

, and

h

be three functions defined as follows:

f(x)=\dfrac{32}{4+x^2+x^4}

g(x)=9+x^2

, and

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

. Identify which of the following statements are correct. (a) The number of integers in the range of

f(x)

8

. (b) The number of integral values of

k

for which

h(f(x))>0

and

h(g(x))<0

for all

x\in\mathbb{R}

20

. (c) The number of integral values of

k

for which

h(f(x))>0

and

h(g(x))<0

for all

x\in\mathbb{R}

19

. (d) The maximum value of

g(f(x))

73