write:(c)(gf)(x)We’llnotputinthedetailinthispartasitworksessentiallythesameasthepreviouspart. (gf)(x)=gf(x)=g2+3xx2=22+3xx21=4+6x2x21=2×2+6x+3NoticethatthisisNOTthesameanswerast

noticethatsincewe’vegotaformulaforg(x)wewentaheadandpluggedthatinfirst.Also
wedidthiskindoffunctionevaluationinthefirstsectionwelookedatforfunctions.Atthetimeitprobablydidn’tseemallthatusefultobelookingatthatkindoffunctionevaluation
yethereitis.Let’sfinishthisproblemout.(fg)(x)=fg(x)=f2×1=2+3(2×1)(2×1)2=2+6x34x24x+1
=1+6x4x2+4×1=4×2+10x2Noticethatthisisverydifferentfromthemultiplication!Rememberthatfunctioncom-positionisNOTfunctionmultiplication.(c)(gf)(x)We’llnotputinthedetailinthispartasitworksessentiallythesameasthepreviouspart.(gf)(x)=gf(x)=g2+3xx2=22+3xx2
1=4+6x2x21=2×2+6x+3NoticethatthisisNOTthesameanswerasthatfromthesecondpart.Inmostcasestheorderinwhichwedothefunctioncompositionwillgivedifferentanswers.©PaulDawkinsAlgebra–220–