(Section 1.6: Combining Functions) 1.6.12 PART E: “DECOMPOSING” COMPOSITE FUNCTIONSExample 8 (“Decomposing” a Composite Function)Find component functionsfand gsuch that f±g()x=3x+1. We want to “decompose” f±g. • Neitherfnor g may be an identity function. For example, do notuse: gx=xand fu=3u+1. This would nottruly be a decomposition.fdoes all the work! x±g:=x±x, our u±²³´³±f:=3u+1fµg³³³³³³³³³´³³³³³³³³³±3x+1fgx²³´µ¶·³§ Solution• We need: =3x+1. • We can think offand g as buttons we are designing on a basic calculator. We need to set upfand g so that, if xis an initial input to Domf±g, and
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