Mathematics

Problem

Consider the function

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

given by

f(x)=\sin x

. a. (i) Show that

f

is not one–one on

\mathbb{R}

. b. (ii) Justify why the restriction of

f

to the interval

\left[-\frac{\pi}{2},\,\frac{\pi}{2}\right]

is invertible. c. (iii) Identify any other interval (different from the one in part (ii)) on which

f

can be made invertible, and explain your choice.