Let and . Consider the function defined by . Is one-one and onto? Justify your…

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

Problem

10. Let

\mathrm{A}=\mathbf{R}-\{3\}

and

\mathrm{B}=\mathbf{R}-\{1\}

. Consider the function

f: \mathrm{A} \rightarrow \mathrm{B}

defined by

f(x)=\left(\frac{x-2}{x-3}\right)

. Is

f

one-one and onto? Justify your answer.