Section 1.5: Misc Exercises
Exercise 1
Show that the function \(f : \mathbb{R}
\rightarrow \{x \in \mathbb{R} : -1 < x < 1\}\) defined
by
\[
f(x) = \frac{-x}{1 + |x|},\quad x \in \mathbb{R}
\]
is one-one and onto function.
Show that the function \(f : \mathbb{R}
\rightarrow \{x \in \mathbb{R} : -1 < x < 1\}\) defined
by
\[
f(x) = \frac{-x}{1 + |x|},\quad x \in \mathbb{R}
\]
is one-one and onto function.