If , , and have the same bounded set as their range, the value of…

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

Problem

f: \mathbb{R} \to \mathbb{R}

f(x) = \frac{x^2 + bx + 1}{x^2 + 2x + b}

(b > 1)

and

f(x), \frac{1}{f(x)}

have the same bounded set as their range, the value of

b

is (1)

2\sqrt{3} - 2

(2)

2\sqrt{3} + 2

(3)

2\sqrt{2} - 2

(4)

2\sqrt{2} + 2