Example 2Let 1( )3f xx³and ( )g xx. Find the domains f and g and then find. (a)fg´(b) fg³(c) fg(d) fg(e) fg(f) fg(g) gf(h) ff(i) ggExample 3Find fghif ( )1xf xx´, 20( )g xxand ( )5h xx´Going forward is one thing. Going backwards is yet another. Example 4 Decompose the function 3( )8h xx³into two non-trivial functions f and g such that hfg. How many unique decompositions can you find? Dfxx433Dgxlxzox2t3xhCx7Hx7gCGfCxltgCxhCxlfCxlglxhashlx7ztTxuldTxnextTxgoxiiiisameasaonxlxzo939gtext_hCxhCxfIX3oµyDhxlx33TfglumSPUDDecomposeinto2functionsglxfxhCxTzTfgCxDhCxhx1x3ttD2hxx3226321
If you’ve ever done something you wish you could undo, then you are alone. I’m kidding, of course. We all have done something we’d like to have back. Although we can’t do that in our own lives, in the world of functions, this is
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