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Diketahui f(x)=2x+1, g(x)=3x dan h(x)=5x−4. Tentukanlah h∘g∘f(x)=...

Pertanyaan

Diketahui f left parenthesis x right parenthesis equals 2 x plus 1, g left parenthesis x right parenthesis equals 3 x dan h left parenthesis x right parenthesis equals 5 x minus 4. Tentukanlah h ring operator g ring operator f left parenthesis x right parenthesis equals...

S. Difhayanti

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. Dr. Hamka

Jawaban terverifikasi

Jawaban

fungsi komposisi dari h ring operator g ring operator f left parenthesis x right parenthesis adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 30 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 11 end table.

Pembahasan

Diketahui :

f left parenthesis x right parenthesis equals 2 x plus 1
g left parenthesis x right parenthesis equals 3 x
h left parenthesis x right parenthesis equals 5 x minus 4

Ditanya :

h ring operator g ring operator f left parenthesis x right parenthesis ?

Jawab:
Menentukan fungsi komposisi dari dari tiga fungsi yaitu h ring operator g ring operator f left parenthesis x right parenthesis, diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell h ring operator g ring operator f left parenthesis x right parenthesis end cell equals cell h open square brackets open parentheses g ring operator f close parentheses left parenthesis x right parenthesis close square brackets end cell row blank equals cell h open square brackets g left parenthesis f left parenthesis x right parenthesis right parenthesis close square brackets end cell row blank equals cell h open square brackets 3 open parentheses 2 x plus 1 close parentheses close square brackets end cell row blank equals cell h open square brackets 6 x plus 3 close square brackets end cell row blank equals cell 5 left parenthesis 6 x plus 3 right parenthesis minus 4 end cell row blank equals cell 30 x plus 15 minus 4 end cell row blank equals cell 30 x plus 11 end cell end table

Jadi, fungsi komposisi dari h ring operator g ring operator f left parenthesis x right parenthesis adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank 30 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank plus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 11 end table.

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