Match the entries in column-I with column-II

MATHEMATICS · Subjective · AP · AP Precalculus · Polynomial and Rational Functions · Polynomial and Rational Functions

Problem

Match the entries in column-I with column-II. Let

f(x)=\frac{x^3-4}{(x-1)^3}

for all

x\in\mathbb{R}-\{1\}

and

h(x)=\frac{x^3+4}{(x+1)^3}

for all

x\in\mathbb{R}-\{-1\}

Column I	Column II	Value
(a) Number of distinct real roots of equation $f(x)=k$ where $k\in[4,\infty)$ can be	(p)	0
(b) Number of distinct real roots of equation $h(x)=k$ where $k\in[1,\infty)$ can be	(q)	1
(c) Number of distinct real roots of equation $f(x)=k$ where $k\in[0,1]$ can be	(r)	2
(d) Number of distinct real roots of equation $h(x)=k$ where $k\in(0,1)$ can be	(s)	3