Consider the function given by

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

Problem

Consider the function

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

given by

f(x)=\dfrac{x}{1+|x|}

. Which of the following statements is true about

f

? (a)

f

is not surjective because its range is

(0,1)

. (b)

f

is not surjective because its range is

(-1,1)

. (c)

f

is surjective because its range is

(-1,1)

. (d)

f

is not surjective because its range is

[-1,1]