Diketahui fungsi f:R→R, g:R→R, dan h:R→R dinyatakan oleh rumus f(x)=3x dan g(x)=x2+3, dan h(x)=3−x. Tunjukkan bahwa (f∘(g∘h))(x)=((f∘g)∘h)(x).

Pertanyaan

Diketahui fungsi begin mathsize 14px style f colon straight real numbers rightwards arrow straight real numbers end stylebegin mathsize 14px style g colon straight real numbers rightwards arrow straight real numbers end style, dan begin mathsize 14px style h colon straight real numbers rightwards arrow straight real numbers end style dinyatakan oleh rumus begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x squared plus 3 end style, dan begin mathsize 14px style h left parenthesis x right parenthesis equals 3 minus x end style.

Tunjukkan bahwa begin mathsize 14px style open parentheses f ring operator open parentheses g ring operator h close parentheses close parentheses left parenthesis x right parenthesis equals open parentheses open parentheses f ring operator g close parentheses ring operator h close parentheses left parenthesis x right parenthesis end style.

A. Rizky

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

terbukti begin mathsize 14px style open parentheses f ring operator open parentheses g ring operator h close parentheses close parentheses left parenthesis x right parenthesis equals open parentheses open parentheses f ring operator g close parentheses ring operator h close parentheses left parenthesis x right parenthesis end style.

Pembahasan

Diketahui fungsi begin mathsize 14px style f colon straight real numbers rightwards arrow straight real numbers end stylebegin mathsize 14px style g colon straight real numbers rightwards arrow straight real numbers end style, dan begin mathsize 14px style h colon straight real numbers rightwards arrow straight real numbers end style dinyatakan oleh rumus begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x squared plus 3 end style, dan begin mathsize 14px style h left parenthesis x right parenthesis equals 3 minus x end style.

Pertama akan dicari begin mathsize 14px style open parentheses f ring operator open parentheses g ring operator h close parentheses close parentheses left parenthesis x right parenthesis end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator open parentheses g ring operator h close parentheses right parenthesis left parenthesis x right parenthesis end cell equals cell open parentheses f ring operator g open parentheses h left parenthesis x right parenthesis close parentheses close parentheses end cell row blank equals cell open parentheses f ring operator g open parentheses 3 minus x close parentheses close parentheses end cell row blank equals cell open parentheses f open parentheses g open parentheses 3 minus x close parentheses close parentheses close parentheses end cell row blank equals cell open parentheses f open parentheses open parentheses 3 minus x close parentheses squared plus 3 close parentheses close parentheses end cell row blank equals cell f open parentheses 12 minus 6 x plus x squared close parentheses end cell row blank equals cell 3 open parentheses 12 minus 6 x plus x squared close parentheses end cell row blank equals cell 3 x squared minus 18 x plus 36 end cell end table end style 

Selanjutnya akan dicari begin mathsize 14px style open parentheses open parentheses f ring operator g close parentheses ring operator h close parentheses left parenthesis x right parenthesis end style dengan terlebih dahulu mencari begin mathsize 14px style open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row blank equals cell f open parentheses x squared plus 3 close parentheses end cell row blank equals cell 3 open parentheses x squared plus 3 close parentheses end cell row blank equals cell 3 x squared plus 9 end cell end table end style 

sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses open parentheses f ring operator g close parentheses ring operator h close parentheses open parentheses x close parentheses end cell equals cell open parentheses open parentheses f ring operator g close parentheses open parentheses h left parenthesis x right parenthesis close parentheses close parentheses end cell row blank equals cell open parentheses f ring operator g close parentheses left parenthesis 3 minus x right parenthesis end cell row blank equals cell 3 open parentheses 3 minus x close parentheses squared plus 9 end cell row blank equals cell 3 open parentheses 9 minus 6 x plus x squared close parentheses plus 9 end cell row blank equals cell 3 x squared minus 18 x plus 36 end cell end table end style 
 

Jadi, terbukti begin mathsize 14px style open parentheses f ring operator open parentheses g ring operator h close parentheses close parentheses left parenthesis x right parenthesis equals open parentheses open parentheses f ring operator g close parentheses ring operator h close parentheses left parenthesis x right parenthesis end style.

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