Mathematics

Problem

Consider the functions

f(x)=\lvert x\rvert

and

g(x)=x^{2}-1

. The graphs of

f

and

g

enclose a bounded region in the plane. What is the exact area of this region? a)

\dfrac{\sqrt5-1}{3}

\dfrac{11+5\sqrt5}{6}

\dfrac{7+5\sqrt5}{6}

\dfrac{7+5\sqrt5}{12}