Section 2: Problem 6 Solution

Working problems is a crucial part of learning mathematics. No one can learn topology merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.

James R. Munkres

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be the function $f(x)=x^{3}-x$ . By restricting the domain and range of $f$ appropriately, obtain from $f$ a bijective function $g$ . Draw the graphs of $g$ and $g^{-l}$ . (There are several possible choices for $g$ .)

For example, $f:\{0\}\rightarrow\{0\}$ . :) The graph is the point $(0,0)$ . Other solutions: $f:\{1,2\}\rightarrow\{0,6\}$ , $f:[-0.5,0.5]\rightarrow[-\frac{3}{8},\frac{3}{8}]$ , $f:(-\infty,-1]\rightarrow(-\infty,0]$ , $f:[1,+\infty)\rightarrow[0,+\infty)$ etc.

Subpages

Section 2: Problem 6 Solution

Section 2: Problem 6 Solution