Roboguru

Diketahui fungsi  f(x)=2x+3. Tentukan (f∘f∘f)(x)!

Pertanyaan

Diketahui fungsi  begin mathsize 14px style f open parentheses x close parentheses equals 2 x plus 3 end style. Tentukan begin mathsize 14px style open parentheses f ring operator f ring operator f close parentheses open parentheses x close parentheses end style!

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator f ring operator f close parentheses open parentheses x close parentheses end cell equals cell f open square brackets f open parentheses f open parentheses x close parentheses close parentheses close square brackets end cell row cell f open parentheses f open parentheses x close parentheses close parentheses end cell equals cell 2 x plus 3 end cell row blank equals cell 2 open parentheses 2 x plus 3 close parentheses plus 3 end cell row blank equals cell 4 x plus 6 plus 3 end cell row blank equals cell 4 x plus 9 end cell row cell f open square brackets f open parentheses f open parentheses x close parentheses close parentheses close square brackets end cell equals cell 2 x plus 3 end cell row blank equals cell 2 open parentheses 4 x plus 9 close parentheses plus 3 end cell row blank equals cell 8 x plus 18 plus 3 end cell row blank equals cell 8 x plus 21 end cell end table end style

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses f ring operator f ring operator f close parentheses end cell end table open parentheses x close parentheses table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 8 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 21 end table end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Herlanda

Mahasiswa/Alumni STKIP PGRI Jombang

Terakhir diupdate 06 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

Pertanyaan yang serupa

Jika: f(x)=2x+3g(x)=x2−4h(x)=3x−2  Tentukan h(x)∘(f∘g)(x).

Pembahasan Soal:

Ingat kembali cara menentukan komposisi dari tiga fungsi.

Terlebih dahulu tentukan nilai (fg)(x).

Perhatikan perhitungan berikut.

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 open parentheses f left parenthesis g left parenthesis x right parenthesis close parentheses end cell row blank equals cell 2 left parenthesis x squared minus 4 right parenthesis plus 3 end cell row blank equals cell 2 x squared minus 8 plus 3 end cell row blank equals cell 2 x squared minus 5 end cell end table end style

Kemudian tentukan h(x)(fg)(x).

Perhatikan perhitungan berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell h left parenthesis x right parenthesis ring operator open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell h left parenthesis f left parenthesis g left parenthesis x right parenthesis right parenthesis right parenthesis end cell row blank equals cell 3 left parenthesis 2 x squared minus 5 right parenthesis minus 2 end cell row blank equals cell 6 x squared minus 15 minus 2 end cell row blank equals cell 6 x squared minus 17 end cell end table end style 

Dengan demikian, diperoleh h(x)(fg)(x)=6x217.

0

Roboguru

Jika diketahui fungsi f(x)=3x−1x+2​,g(x)=2x2+5,danh(x)=3x−4​,maka(f∘g∘h)(x)=...

Pembahasan Soal:

Penyelesaian:

f left parenthesis x right parenthesis equals fraction numerator x plus 2 over denominator 3 x minus 1 end fraction comma space g left parenthesis x right parenthesis equals 2 x squared plus 5 comma space h left parenthesis x right parenthesis equals square root of 3 x minus 4 end root  left parenthesis f ring operator g ring operator h right parenthesis left parenthesis x right parenthesis equals left parenthesis f ring operator left parenthesis g ring operator h right parenthesis right parenthesis left parenthesis x right parenthesis    m i s a l space left parenthesis g ring operator h right parenthesis left parenthesis x right parenthesis equals q left parenthesis x right parenthesis  left parenthesis g ring operator h right parenthesis left parenthesis x right parenthesis equals g left parenthesis h left parenthesis x right parenthesis right parenthesis  equals g left parenthesis square root of 3 x minus 4 end root right parenthesis  equals 2 left parenthesis square root of 3 x minus 4 end root right parenthesis squared plus 5  equals 2 left parenthesis 3 x minus 4 right parenthesis plus 5  equals 6 x minus 8 plus 5 equals 6 x minus 3    q left parenthesis x right parenthesis equals 6 x minus 3  left parenthesis f ring operator g ring operator h right parenthesis left parenthesis x right parenthesis equals left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis  equals f left parenthesis 6 x minus 3 right parenthesis  equals fraction numerator 6 x minus 3 plus 2 over denominator 3 left parenthesis 6 x minus 3 right parenthesis minus 1 end fraction  equals fraction numerator 6 x minus 1 over denominator 18 x minus 9 minus 1 end fraction equals fraction numerator 6 x minus 1 over denominator 18 x minus 10 end fraction

0

Roboguru

Diketahui fungsi f(x)=2x−1, fungsi g(x)=4x+5 dan fungsi h(x)=2x−3 maka rumus fungsi komposisi (f∘g∘h)(x) adalah ....

Pembahasan Soal:

Diketahui:

fungsi begin mathsize 14px style straight f left parenthesis straight x right parenthesis equals 2 straight x minus 1 end style, fungsi begin mathsize 14px style g left parenthesis straight x right parenthesis equals 4 straight x plus 5 end style dan fungsi begin mathsize 14px style h left parenthesis straight x right parenthesis equals 2 straight x minus 3 end style.

Ditanya:

fungsi komposisi begin mathsize 14px style left parenthesis straight f ring operator straight g ring operator straight h right parenthesis left parenthesis straight x right parenthesis end style 

Jawaban:

Dengan konsep komposisi fungsi:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight f ring operator straight g ring operator straight h right parenthesis left parenthesis straight x right parenthesis end cell equals cell straight f left parenthesis straight g left parenthesis straight h left parenthesis straight x right parenthesis right parenthesis right parenthesis end cell row blank equals cell straight f left parenthesis straight g left parenthesis 2 straight x minus 3 right parenthesis right parenthesis end cell row blank equals cell straight f left parenthesis 4 left parenthesis 2 straight x minus 3 right parenthesis plus 5 right parenthesis end cell row blank equals cell straight f left parenthesis 8 straight x minus 12 plus 5 right parenthesis end cell row blank equals cell straight f left parenthesis 8 straight x minus 7 right parenthesis end cell row blank equals cell 2 left parenthesis 8 straight x minus 7 right parenthesis minus 1 end cell row blank equals cell 16 straight x minus 14 minus 1 end cell row blank equals cell 16 straight x minus 15 end cell end table end style 

Dengan demikian, Rumus fungsi  begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis straight f ring operator straight g ring operator straight h right parenthesis left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 16 end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank straight x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 15 end table end style.

0

Roboguru

Jika diketahui fungsi f(x)=3x+5, g(x)=2x dan h(x)=x2+2, tentukan: a. f∘g b. g∘h c. (f∘g)∘h d. f∘(g∘h) Apa yang dapat Anda simpulkan dari hasil tersebut? Dapatkah aturan tersebut berlaku pada fung...

Pembahasan Soal:

a. begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank f end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank ring operator end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank g end table end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f ring operator g end cell equals cell f open parentheses g open parentheses x close parentheses close parentheses end cell row cell f ring operator g end cell equals cell f open parentheses 2 x close parentheses end cell row cell f ring operator g end cell equals cell 3 open parentheses 2 x close parentheses plus 5 end cell row cell f ring operator g end cell equals cell 6 x plus 5 end cell end table end style

b. begin mathsize 14px style g ring operator h end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g ring operator h end cell equals cell g open parentheses h open parentheses x close parentheses close parentheses end cell row cell g ring operator h end cell equals cell g open parentheses x squared plus 2 close parentheses end cell row cell g ring operator h end cell equals cell 2 open parentheses x squared plus 2 close parentheses end cell row cell g ring operator h end cell equals cell 2 x squared plus 4 end cell end table end style 

c. begin mathsize 14px style open parentheses f ring operator g close parentheses ring operator h end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis ring operator h end cell equals cell open parentheses f open parentheses g open parentheses x close parentheses close parentheses close parentheses ring operator h end cell row cell left parenthesis f ring operator g right parenthesis ring operator h end cell equals cell open parentheses 6 x plus 5 close parentheses ring operator h end cell row cell left parenthesis f ring operator g right parenthesis ring operator h end cell equals cell 6 open parentheses h open parentheses x close parentheses close parentheses plus 5 end cell row cell left parenthesis f ring operator g right parenthesis ring operator h end cell equals cell 6 open parentheses x squared plus 2 close parentheses plus 5 end cell row cell left parenthesis f ring operator g right parenthesis ring operator h end cell equals cell 6 x squared plus 12 plus 5 end cell row cell left parenthesis f ring operator g right parenthesis ring operator h end cell equals cell 6 x squared plus 17 end cell end table end style

d. begin mathsize 14px style f ring operator open parentheses g ring operator h close parentheses end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f ring operator left parenthesis g ring operator h right parenthesis end cell equals cell f ring operator left parenthesis g open parentheses h open parentheses x close parentheses close parentheses right parenthesis end cell row cell f ring operator left parenthesis g ring operator h right parenthesis end cell equals cell f ring operator open parentheses 2 x squared plus 4 close parentheses end cell row cell f ring operator left parenthesis g ring operator h right parenthesis end cell equals cell f open parentheses 2 x squared plus 4 close parentheses end cell row cell f ring operator left parenthesis g ring operator h right parenthesis end cell equals cell 3 open parentheses 2 x squared plus 4 close parentheses plus 5 end cell row cell f ring operator left parenthesis g ring operator h right parenthesis end cell equals cell 6 x squared plus 12 plus 5 end cell row cell f ring operator left parenthesis g ring operator h right parenthesis end cell equals cell 6 x squared plus 17 end cell end table end style

Ternyata jawaban pada soal c dan d adalah sama yaitu aturan begin mathsize 14px style f ring operator open parentheses g ring operator h close parentheses end style dan begin mathsize 14px style open parentheses f ring operator g close parentheses ring operator h end style maka dapat disimpulkan bawaha begin mathsize 14px style left parenthesis f ring operator g right parenthesis ring operator h equals f ring operator left parenthesis g ring operator h right parenthesis end style atau biasa di sebut aturan asosiatif dan berlaku untuk fungsi yang lain.

0

Roboguru

Diketahui f(x) = 2x - 4, g(x) = x - 5, dan h(x) = 4 - 3x dengan x∈R . Maka,   ....

Pembahasan Soal:

Pertama, kita cari begin mathsize 14px style open parentheses straight f ring operator straight g close parentheses open parentheses straight x close parentheses end style .

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses straight f ring operator straight g close parentheses open parentheses straight x close parentheses end cell equals cell straight f open parentheses straight g open parentheses straight x close parentheses close parentheses end cell row blank equals cell straight f open parentheses straight x minus 5 close parentheses end cell row blank equals cell 2 open parentheses straight x minus 5 close parentheses minus 4 end cell row blank equals cell 2 straight x minus 10 minus 4 end cell row blank equals cell 2 straight x minus 14 end cell end table end style 

Misalkan begin mathsize 14px style open parentheses straight f ring operator straight g close parentheses open parentheses straight x close parentheses end style  =p (x)  .

Maka,

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses open parentheses straight f ring operator straight g close parentheses ring operator straight h close parentheses open parentheses straight x close parentheses end cell equals cell open parentheses straight p ring operator straight h close parentheses open parentheses straight x close parentheses end cell row blank equals cell straight p open parentheses straight h open parentheses straight x close parentheses close parentheses end cell row blank equals cell straight p open parentheses 4 minus 3 straight x close parentheses end cell row blank equals cell 2 open parentheses 4 minus 3 straight x close parentheses minus 14 end cell row blank equals cell 8 minus 6 straight x minus 14 end cell row blank equals cell negative 6 straight x minus 6 end cell end table end style 

Perhatikan bahwa kita juga bisa mencarinya dengan cara berikut.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses open parentheses straight f ring operator straight g close parentheses ring operator straight h close parentheses open parentheses straight x close parentheses end cell equals cell open parentheses straight f ring operator open parentheses straight g ring operator straight h close parentheses close parentheses open parentheses straight x close parentheses end cell row blank equals cell straight f open parentheses straight g open parentheses straight h open parentheses straight x close parentheses close parentheses close parentheses end cell row blank equals cell straight f open parentheses straight g open parentheses 4 minus 3 straight x close parentheses close parentheses end cell row blank equals cell straight f open parentheses 4 minus 3 straight x minus 5 close parentheses end cell row blank equals cell straight f open parentheses negative 3 straight x minus 1 close parentheses end cell row blank equals cell 2 open parentheses negative 3 straight x minus 1 close parentheses minus 4 end cell row blank equals cell negative 6 straight x minus 2 minus 4 end cell row blank equals cell negative 6 straight x minus 6 end cell end table end style 

Jadi, jawabannya adalah C.

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

Tapi Roboguru masih mau belajar. Menurut kamu pembahasan kali ini sudah membantu, belum?

Membantu

Kurang Membantu

Apakah pembahasan ini membantu?

Belum menemukan yang kamu cari?

Post pertanyaanmu ke Tanya Jawab, yuk

Mau Bertanya

RUANGGURU HQ

Jl. Dr. Saharjo No.161, Manggarai Selatan, Tebet, Kota Jakarta Selatan, Daerah Khusus Ibukota Jakarta 12860

Coba GRATIS Aplikasi Ruangguru

Produk Ruangguru

Produk Lainnya

Hubungi Kami

Ikuti Kami

©2021 Ruangguru. All Rights Reserved