The function is defined for all real satisfying and

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

The function

y=\dfrac{1}{x}

is defined for all real

x

satisfying

|x-1|<2

and

x\ne0

. Determine the range of

y

. (a)

(-\infty,-\tfrac13)\cup(1,\infty)

(b)

(-\infty,-1]\cup\left[\tfrac13,\infty\right)

(c)

(-\infty,-1)\cup\left(\tfrac13,\infty\right)

(d)

(-1,0)\cup\left(0,\tfrac13\right)