Let . If is onto, find the set . Here and represent the fractional-part and…

MATHEMATICS · Single correct · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

Let

f(x)=\frac{x-[x]}{1+x-[x]}

. If

f:\mathbb{R}\to A

is onto, find the set

A

. Here

\{\cdot\}

and

[\cdot]

represent the fractional-part and greatest-integer functions, respectively. (a)

\left(0,\frac{1}{2}\right]

(b)

\left[0,\frac{1}{2}\right]

(c)

\left[0,\frac{1}{2}\right)

(d)

\left(0,\frac{1}{2}\right)