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Jika f(x+2)=4x+1 dan (f∘g)(x)=4x+17, maka g(4)=....

Pertanyaan

Jika begin mathsize 14px style f open parentheses x plus 2 close parentheses equals 4 x plus 1 end style dan begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 4 x plus 17 end style, maka begin mathsize 14px style g open parentheses 4 close parentheses end stylebegin mathsize 14px style equals end style....

Pembahasan Soal:

Diketahui fungsi begin mathsize 14px style f open parentheses x plus 2 close parentheses equals 4 x plus 1 end style dan begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 4 x plus 17 end style. Misalkan begin mathsize 14px style x plus 2 equals y end style, diperoleh

begin mathsize 14px style x equals y minus 2 end style

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x plus 2 close parentheses end cell equals cell 4 x plus 1 end cell row cell f open parentheses y close parentheses end cell equals cell 4 open parentheses y minus 2 close parentheses plus 1 end cell row cell f open parentheses y close parentheses end cell equals cell 4 y minus 8 plus 1 end cell row cell f open parentheses y close parentheses end cell equals cell 4 y minus 7 end cell end table end style

Untuk begin mathsize 14px style y equals x end style, diperoleh

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 cell open parentheses x close parentheses 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 4 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 minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank 7 end table end style

Untuk begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 4 x plus 17 end style, diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 4 x plus 17 end cell row cell 4 open parentheses g open parentheses x close parentheses close parentheses minus 7 end cell equals cell 4 x plus 17 end cell row cell 4 open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 4 x plus 17 plus 7 end cell row cell g open parentheses x close parentheses end cell equals cell fraction numerator 4 x plus 24 over denominator 4 end fraction end cell end table end style

Untuk begin mathsize 14px style x equals 4 end style, diperoleh

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses 4 close parentheses end cell equals cell fraction numerator 4 open parentheses 4 close parentheses plus 24 over denominator 4 end fraction end cell row blank equals cell 40 over 4 end cell row blank equals 10 end table end style

Jadi, begin mathsize 14px style g open parentheses 4 close parentheses end stylebegin mathsize 14px style equals end stylebegin mathsize 14px style 10 end style.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

Y. Umi

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 06 Oktober 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui f(x)=2x−13x​ dan g(x)=3x+12x​. (f∘g)(x)=....

Pembahasan Soal:

Diketahui  dan 

begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses end style

                begin mathsize 14px style equals f open parentheses fraction numerator 2 x over denominator 3 x plus 1 end fraction close parentheses equals fraction numerator 3 open parentheses begin display style fraction numerator 2 x over denominator 3 x plus 1 end fraction end style close parentheses over denominator 2 open parentheses begin display style fraction numerator 2 x over denominator 3 x plus 1 end fraction end style close parentheses minus 1 end fraction cross times fraction numerator 3 x plus 1 over denominator 3 x plus 1 end fraction equals fraction numerator 3 left parenthesis 2 x right parenthesis over denominator 2 left parenthesis 2 x right parenthesis minus left parenthesis 3 x plus 1 right parenthesis end fraction equals fraction numerator 6 x over denominator 4 x minus 3 x minus 1 end fraction equals fraction numerator 6 x over denominator x minus 1 end fraction end style

jadi, jawabannya  

0

Roboguru

Diketahui f(x)=cos2(x)−sin2(x) dan g(x)=x2+41​. Nilai (g∘f)(3π​)=....

Pembahasan Soal:

Ingat!

begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals g left parenthesis f left parenthesis x right parenthesis right parenthesis end style, artinya begin mathsize 14px style f end style dimasukkan ke begin mathsize 14px style g end style 

Berdasarkan konsep tersebut akan dicari begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis straight pi over 3 right parenthesis equals... end style  

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell cos squared left parenthesis x right parenthesis minus sin squared left parenthesis x right parenthesis end cell row cell f left parenthesis straight pi over 3 right parenthesis end cell equals cell cos squared left parenthesis straight pi over 3 right parenthesis minus sin squared left parenthesis straight pi over 3 right parenthesis end cell row blank equals cell left parenthesis 1 half right parenthesis squared minus left parenthesis 1 half square root of 3 right parenthesis squared equals fraction numerator 1 over denominator 4 end fraction minus 3 over 4 end cell row blank equals cell negative 2 over 4 end cell row blank equals cell negative 1 half end cell end table end style 

maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis straight pi over 3 right parenthesis end cell equals cell g left parenthesis f left parenthesis straight pi over 3 right parenthesis right parenthesis end cell row blank equals cell g left parenthesis negative 1 half right parenthesis end cell row blank equals cell left parenthesis negative 1 half right parenthesis squared plus fraction numerator 1 over denominator 4 end fraction equals 1 fourth plus 1 fourth end cell row blank equals cell 2 over 4 end cell row blank equals cell 1 half end cell end table end style 

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Diketahui fungsi f:R→R dan g:R→R ditentukan oleh f(x)=2x2+6x+4 dan g(x)=x−3, maka (f∘g)(x)=…

Pembahasan Soal:

Ingat kembali bahwa open parentheses f ring operator g close parentheses open parentheses x close parentheses artinya g dimasukkan ke f sehingga open parentheses f ring operator g close parentheses open parentheses x close parentheses equals f open parentheses g open parentheses x close parentheses close parentheses.

Diketahui f open parentheses x close parentheses equals 2 x squared plus 6 x plus 4 dan g open parentheses x close parentheses equals x minus 3, maka

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 x minus 3 close parentheses end cell row blank equals cell 2 open parentheses x minus 3 close parentheses squared plus 6 open parentheses x minus 3 close parentheses plus 4 end cell row blank equals cell 2 open parentheses x squared minus 6 x plus 9 close parentheses plus 6 x minus 18 plus 4 end cell row blank equals cell 2 x squared minus 12 x plus 18 plus 6 x minus 18 plus 4 end cell row blank equals cell 2 x squared minus 12 x plus 6 x plus 18 minus 18 plus 4 end cell row blank equals cell 2 x squared minus 6 x plus 4 end cell end table

Dengan demikian, open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 2 x squared minus 6 x plus 4.

0

Roboguru

Diketahui f(x)=2x−5, g(x)=3−x, dan (f∘g)(m)=7. Nilai m=....

Pembahasan Soal:

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x minus 5 end stylebegin mathsize 14px style g left parenthesis x right parenthesis equals 3 minus x end style, dan begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis m right parenthesis equals 7 end style. Sehingga diperoleh

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 2 open parentheses g open parentheses x close parentheses close parentheses minus 5 end cell row blank equals cell 2 open parentheses 3 minus x close parentheses minus 5 end cell row blank equals cell 6 minus 2 x minus 5 end cell row blank equals cell 1 minus 2 x end cell row blank blank blank row blank blank blank end table end style

Untuk begin mathsize 14px style x equals m 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 m close parentheses end cell equals cell 1 minus 2 open parentheses m close parentheses end cell row 7 equals cell 1 minus 2 m end cell row cell 2 m end cell equals cell 1 minus 7 end cell row cell 2 m end cell equals cell negative 6 end cell row m equals cell fraction numerator negative 6 over denominator 2 end fraction end cell row m equals cell negative 3 end cell end table end style

Jafi, nilai begin mathsize 14px style m equals negative 3 end style.

0

Roboguru

Diketahui fungsi f(x)=2x2−3x+4 dan g(x)=4x−5. Nilai dari (g∘f)(2) adalah ....

Pembahasan Soal:

Konposisi dua fungsi.

Diketahui f open parentheses x close parentheses equals 2 x squared minus 3 x plus 4 dan g open parentheses x close parentheses equals 4 x minus 5, akan ditentukan open parentheses g ring operator f close parentheses open parentheses 2 close parentheses.

Terlebih dahulu tentukan open parentheses g ring operator f close parentheses open parentheses x close parentheses.

Perhatikan perhitungan berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses 2 x squared minus 3 x plus 4 close parentheses end cell row blank equals cell 4 open parentheses 2 x squared minus 3 x plus 4 close parentheses minus 5 end cell row blank equals cell 8 x squared minus 12 x plus 16 minus 5 end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell 8 x squared minus 12 x plus 11 end cell end table

Sehingga nilai open parentheses g ring operator f close parentheses open parentheses 2 close parentheses dapat dihitung sebagai berikut.

table attributes columnalign right center left columnspacing 2px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell 8 x squared minus 12 x plus 11 end cell row cell open parentheses g ring operator f close parentheses open parentheses 2 close parentheses end cell equals cell 8 open parentheses 2 close parentheses squared minus 12 open parentheses 2 close parentheses plus 11 end cell row blank equals cell 8 open parentheses 4 close parentheses minus 24 plus 11 end cell row blank equals cell 32 minus 24 plus 11 end cell row cell open parentheses g ring operator f close parentheses open parentheses 2 close parentheses end cell equals 19 end table 

Jadi, diperoleh open parentheses g ring operator f close parentheses open parentheses 2 close parentheses equals 19.

0

Roboguru

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