Consider the function defined by

MATHEMATICS · Subjective · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Consider the function

f: \mathbb{R}\setminus\{1\} \to \mathbb{R}

defined by

f(x)=\dfrac{2x}{x-1}

. Show that

f

is not surjective and state the real number that is not in its range.