Tuesday, December 15, 2015

Composition of two functions GeoGebra

Composition of two functions #GeoGebra, this is an interesting applet on #Mathematics

Drag x to vary the input for function g.
-Suggest possible domains of g for fg to be defined. In particular, what's the Maximal domain?
-What's the corresponding range?
-Look at the green line. What's the Domain of fg?
-Are functions fg and gf the same?
My suggested Answer:
corresponding range of f is >0.2
i don't understand the rest :)
i don't understand the rest :)

Exploring Range of composite functions

-You may key in the functions f and g box to vary the functions.
-Move the segment CD to select the respective domain for the first function f.

(a) how the range of the function g changes with the change in the domain of f ?
(b) What does the green highlighted portion represent?
(c) how the output gf(x) relates to the output of g?
(compare range of gf to range of g, are the two sets necessarily the same)?