Roboguru

Diketahui fungsi , dan . Nilai fungsi adalah ..

Pertanyaan

Diketahui fungsispace left parenthesis f o g right parenthesis left parenthesis x right parenthesis equals 4 x squared minus 2 x plus 3 , dan g left parenthesis x right parenthesis equals 2 x plus 1. Nilai fungsi f left parenthesis 2 right parenthesis spaceadalah ..

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell space left parenthesis f o g right parenthesis left parenthesis x right parenthesis end cell equals cell 4 x squared minus 2 x plus 3 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 4 x squared minus 2 x plus 3 end cell row cell f open parentheses 2 x plus 1 close parentheses end cell equals cell 4 x squared minus 2 x plus 3 end cell end table 

kita misalkan:

2 x plus 1 equals y rightwards arrow x equals fraction numerator y minus 1 over denominator 2 end fraction , sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses 2 x plus 1 close parentheses end cell equals cell 4 x blank squared minus 2 x plus 3 space end cell row cell f open parentheses y close parentheses end cell equals cell 4 open parentheses fraction numerator y minus 1 over denominator 2 end fraction close parentheses blank squared minus 2 open parentheses fraction numerator y minus 1 over denominator 2 end fraction close parentheses plus 3 end cell row cell f open parentheses y close parentheses end cell equals cell y blank squared minus 2 y plus 1 minus y plus 1 plus 3 space end cell row cell f open parentheses y close parentheses end cell equals cell y blank squared minus 3 y plus 5 end cell row cell f open parentheses x close parentheses end cell equals cell x squared minus 3 x plus 5 end cell end table 

maka f left parenthesis 2 right parenthesis space:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell x squared minus 3 x plus 5 end cell row cell f open parentheses 2 close parentheses end cell equals cell open parentheses 2 close parentheses squared minus 3 open parentheses 2 close parentheses plus 5 end cell row blank equals cell 4 minus 6 plus 5 end cell row blank equals 3 end table

Jadi, Nilai fungsi f left parenthesis 2 right parenthesis spaceadalah 3

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

M. Nasrullah

Mahasiswa/Alumni Universitas Negeri Makassar

Terakhir diupdate 05 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui  dan  Tentukan  dan  !

Pembahasan Soal:

misal: begin mathsize 14px style x plus 3 equals a space rightwards double arrow space x equals a minus 3 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 2 x squared plus 8 x plus 9 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 2 x squared plus 8 x plus 9 end cell row cell f open parentheses x plus 3 close parentheses end cell equals cell 2 x squared plus 8 x plus 9 end cell end table end style 

substitusi pemisalan tadi

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x plus 3 close parentheses end cell equals cell 2 x squared plus 8 x plus 9 end cell row cell f open parentheses a close parentheses end cell equals cell 2 open parentheses a minus 3 close parentheses squared plus 8 open parentheses a minus 3 close parentheses plus 9 end cell row cell f open parentheses a close parentheses end cell equals cell 2 open parentheses a squared minus 6 a plus 9 close parentheses plus 8 a minus 24 plus 9 end cell row cell f open parentheses a close parentheses end cell equals cell 2 a squared minus 12 a plus 18 plus 8 a minus 15 end cell row cell f open parentheses a close parentheses end cell equals cell 2 a squared minus 4 a plus 3 end cell end table end style

Jadi, begin mathsize 14px style f open parentheses x close parentheses equals 2 x squared minus 4 x plus 3 end style.  

0

Roboguru

Jika (f∘g)(x)=9x2+6x−5 dan g(x)=3x+1, maka f−1(x)=...

Pembahasan Soal:

Diketahui (fg)(x)=9x2+6x5 dan g(x)=3x+1, maka:

(fg)(x)9x2+6x5f(3x+1)misal3x+1f(3(3y1)+1)f(y)f(x)=========f(g(x))f(3x+1)9x2+6x5y,makax=3y19(3y1)2+6(3y1)59(9y22y+1)+2(y1)5y22y+1+2y25y26x26 

Untuk menentukan f1(x), maka:

yx2xf1(x)====x26y+6±y+6±x+6 

Dengan demikian, f1(x)=±x+6.

0

Roboguru

Fungsi  dan  ditentukan oleh  dan . maka  sama dengan ....

Pembahasan Soal:

Fungsi begin mathsize 14px style f colon space R rightwards arrow R end style dan begin mathsize 14px style g colon space R rightwards arrow R end style ditentukan oleh begin mathsize 14px style g open parentheses x close parentheses equals x squared plus 1 end style dan begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 2 x squared minus 1 end style. maka begin mathsize 14px style f open parentheses x close parentheses end style sama dengan .... 

Buat pemisalan dulu: 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x squared plus 1 end cell equals a row cell x squared end cell equals cell a minus 1 end cell row x equals cell square root of a minus 1 end root end cell end table end style 

Dari definisi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses 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 2 x squared minus 1 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 2 x squared minus 1 end cell row cell f open parentheses x squared plus 1 close parentheses end cell equals cell 2 x squared minus 1 end cell end table end style 

Masukkan pemisalan tadi, didapat:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x squared plus 1 close parentheses end cell equals cell 2 x squared minus 1 end cell row cell f open parentheses a close parentheses end cell equals cell 2 open parentheses square root of a minus 1 end root close parentheses squared minus 1 end cell row blank equals cell 2 open parentheses a minus 1 close parentheses minus 1 end cell row blank equals cell 2 a minus 2 minus 1 end cell row cell f open parentheses a close parentheses end cell equals cell 2 a minus 3 end cell end table end style 

Maka, begin mathsize 14px style f open parentheses x close parentheses equals 2 x minus 3 end style.

Jadi, jawaban yang tepat adalah C.

0

Roboguru

Jika  dan  tentukan: a.  b.

Pembahasan Soal:

Diketahui g open parentheses x close parentheses equals x plus 3 dan open parentheses f ring operator g close parentheses open parentheses x close parentheses equals x squared minus 4, misalkan y equals x plus 3 maka x equals y minus 3 dengan menggunakan konsep komposisi fungsi maka diperoleh:

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 x squared minus 4 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell x squared minus 4 end cell row cell f open parentheses x plus 3 close parentheses end cell equals cell x squared minus 4 end cell row cell f open parentheses y close parentheses end cell equals cell open parentheses y minus 3 close parentheses squared minus 4 end cell row blank equals cell open parentheses y squared minus 6 y plus 9 close parentheses minus 4 end cell row cell f open parentheses y close parentheses end cell equals cell y squared minus 6 y plus 5 end cell row cell f open parentheses x close parentheses end cell equals cell x squared minus 6 x plus 5 end cell end table 

a. Jadi fungsi f open parentheses x close parentheses adalah f open parentheses x close parentheses equals x squared minus 6 x plus 5 

b. Substitusikan x equals x minus 2 maka diperoleh:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell x squared minus 6 x plus 5 end cell row cell f open parentheses x minus 2 close parentheses end cell equals cell open parentheses x minus 2 close parentheses squared minus 6 open parentheses x minus 2 close parentheses plus 5 end cell row blank equals cell open parentheses x squared minus 4 x plus 4 close parentheses minus 6 open parentheses x minus 2 close parentheses plus 5 end cell row blank equals cell x squared minus 4 x plus 4 minus 6 x plus 2 plus 5 end cell row blank equals cell x squared minus 10 x plus 11 end cell end table  

Dengan demikian diperoleh fungsi 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 minus 2 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 x end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell blank squared end cell 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 10 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 11.

0

Roboguru

Jika diketahui  dan , maka  adalah

Pembahasan Soal:

begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses equals x squared plus 2 x end style dan begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x minus 1 end style, maka

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell x squared plus 2 x end cell row cell g open parentheses f open parentheses x close parentheses close parentheses end cell equals cell x squared plus 2 x end cell row cell g open parentheses 3 x minus 1 close parentheses end cell equals cell x squared plus 2 x end cell row cell misal space 3 x minus 1 end cell equals cell a comma space maka end cell row cell 3 x end cell equals cell a plus 1 end cell row x equals cell fraction numerator a plus 1 over denominator 3 end fraction comma space sehingga end cell row cell g left parenthesis a right parenthesis end cell equals cell open parentheses fraction numerator a plus 1 over denominator 3 end fraction close parentheses squared plus 2 open parentheses fraction numerator a plus 1 over denominator 3 end fraction close parentheses end cell row cell g left parenthesis a right parenthesis end cell equals cell fraction numerator a squared plus 2 a plus 1 over denominator 9 end fraction plus fraction numerator 2 a plus 2 over denominator 3 end fraction end cell row cell g left parenthesis a right parenthesis end cell equals cell fraction numerator a squared plus 2 a plus 1 over denominator 9 end fraction plus fraction numerator 6 a plus 6 over denominator 9 end fraction end cell row cell g left parenthesis a right parenthesis end cell equals cell fraction numerator a squared plus 8 a plus 7 over denominator 9 end fraction end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator x squared plus 8 x plus 7 over denominator 9 end fraction end cell end table end style 

Jadi, begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator x squared plus 8 x plus 7 over denominator 9 end fraction end style

0

Roboguru

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