Let be given by

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

Problem

Let

f:\mathbb{R}\setminus\{-2-\sqrt{3},-2+\sqrt{3}\}\to\mathbb{R}

be given by

f(x)=\frac{x^2+4x+5}{x^2+4x+1}

. The range of

f

is: (a)

(-\infty,-\tfrac{1}{3})\cup[1,\infty)

(b)

\mathbb{R}\setminus\{-\tfrac{1}{3},1\}

(c)

(-\infty,-\tfrac{1}{3}]\cup(1,\infty)

(d)

(-\infty,-\tfrac{1}{3})\cup(1,\infty)