'Round trips' in maths? non-invertable operations
- Judah L Schwartz
Put in a function of one variable f(x) that can depend on up to three parameters a, b and c. You can use the sliders to set the values of these parameters. Why is the square of the square root of f(x) not always [i.e. only sometimes] equal to the square root of the square of f(x) ? Why is the natural logarithm of e^[f(x)] not always [i.e. only sometimes] equal to e^[ln(f(x)] ? Can you think of other mathematical 'Round trips'? What questions could / would you ask your students based on this applet ?