AS/A2 Pure 1 Pure 3

P2 Topic 2: Functions
Functions and their inverses 2
Use this applet to explore the composition of functions with their inverses. Move the red square. If f(x) and g(x) are inverses then gf(x) should equal x. Try each of the 14 combinations provided. Why is it that sometimes gf(x) is not x?

Summary The trigonometrical functions cause difficulties unless the domain for the inverse function is restricted. The same applies to the square and square root functions. Note that the functions "take from" (Combination 3) and "divide into" (Combination 6) are self inverses. Based on free Java applets from JavaMath