Diketahui fungsi-fungsi f: R→R, g: R→R, h: R→R. Masing-masing ditentukan dengan rumus f(x)=x−1, g(x)=2x dan h(x)=x2. Buktikan bahwa (f∘(g∘h))(x)=(f∘g(∘h))(x)!

Pertanyaan

Diketahui fungsi-fungsi begin mathsize 14px style f colon space R rightwards arrow R comma space g colon space R rightwards arrow R comma space h colon space R rightwards arrow R end style. Masing-masing ditentukan dengan rumus begin mathsize 14px style f open parentheses x close parentheses equals x minus 1 end stylebegin mathsize 14px style g left parenthesis x right parenthesis equals 2 x end style dan begin mathsize 14px style h left parenthesis x right parenthesis equals x squared end style. Buktikan bahwa begin mathsize 14px style open parentheses f ring operator open parentheses g ring operator h close parentheses close parentheses open parentheses x close parentheses equals open parentheses f ring operator g open parentheses ring operator h close parentheses close parentheses open parentheses x close parentheses end style

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Pembahasan

Menentukan begin mathsize 14px style left parenthesis f ring operator open parentheses g ring operator h close parentheses right parenthesis 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 g ring operator h close parentheses open parentheses x close parentheses end cell equals cell g open parentheses h open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses x squared close parentheses end cell row blank equals cell 2 x squared end cell 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 f open parentheses 2 x squared close parentheses end cell row blank equals cell 2 x squared minus 1 end cell end table end style 

Menentukan begin mathsize 14px style left parenthesis f ring operator g open parentheses ring operator h close parentheses right parenthesis 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 open parentheses x close parentheses end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row blank equals cell f open parentheses 2 x close parentheses end cell row blank equals cell 2 x minus 1 end cell row cell left parenthesis f ring operator g open parentheses ring operator h close parentheses right parenthesis left parenthesis x right parenthesis end cell equals cell f open parentheses g open parentheses h open parentheses x close parentheses close parentheses close parentheses end cell row blank equals cell f open parentheses g open parentheses x squared close parentheses close parentheses end cell row blank equals cell 2 x squared minus 1 end cell end table end style 

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

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