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Diketahui fungsi  f: R→R dan g: R→R dengan f(x)=3x−2 dan g(x)=x2−2x+5. Tentukan f(g(x)) dan g(f(x))!

Pertanyaan

Diketahui fungsi Error converting from MathML to accessible text. dan begin mathsize 14px style g colon space text R→R end text end style dengan begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x minus 2 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x squared minus 2 x plus 5 end style. Tentukan begin mathsize 14px style f left parenthesis g left parenthesis x right parenthesis right parenthesis end style dan begin mathsize 14px style g left parenthesis f left parenthesis x right parenthesis right parenthesis end style!

 

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Pembahasan

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x minus 2 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x squared minus 2 x plus 5 end style.

Fungsi komposisi begin mathsize 14px style f left parenthesis g left parenthesis x right parenthesis right parenthesis end style adalah,

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell f open parentheses x squared minus 2 x plus 5 close parentheses end cell row blank equals cell 3 open parentheses x squared minus 2 x plus 5 close parentheses minus 2 end cell row blank equals cell 3 x squared minus 6 x plus 15 minus 2 end cell row blank equals cell 3 x squared minus 6 x plus 13 end cell end table 

Fungsi komposisi begin mathsize 14px style g left parenthesis f left parenthesis x right parenthesis right parenthesis end style yaitu,

table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses f left parenthesis x right parenthesis close parentheses end cell equals cell g open parentheses 3 x minus 2 close parentheses end cell row blank equals cell open parentheses 3 x minus 2 close parentheses squared minus 2 open parentheses 3 x minus 2 close parentheses plus 5 end cell row blank equals cell 9 x squared minus 12 x plus 4 minus 6 x plus 4 plus 5 end cell row blank equals cell 9 x squared minus 18 x plus 13 end cell end table

jadi fungsi komposisi begin mathsize 14px style f left parenthesis g left parenthesis x right parenthesis right parenthesis end style adalah Error converting from MathML to accessible text. dan fungsi komposisi begin mathsize 14px style g left parenthesis f left parenthesis x right parenthesis right parenthesis end style adalah Error converting from MathML to accessible text.

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Tentukanlah bahwa jika I(x)=x dan f(x)=x+4x​ dengan x=4 maka (I∘f)(x)=(f∘I)(x) .

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