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Pertanyaan

Diketahui f left parenthesis x right parenthesis equals 2 x minus 3 dan open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals 4 x minus 9. Nilai dari g to the power of negative 1 end exponent left parenthesis 3 right parenthesis equals... 

Pembahasan Soal:

Diketahui f left parenthesis x right parenthesis equals 2 x minus 3 dan open parentheses g ring operator f close parentheses left parenthesis x right parenthesis equals 4 x minus 9. Maka:

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses left parenthesis x right parenthesis end cell equals cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell row cell 4 x minus 9 end cell equals cell g left parenthesis 2 x minus 3 right parenthesis end cell row cell g left parenthesis 2 x minus 3 right parenthesis end cell equals cell 4 x minus 9 end cell row cell g left parenthesis 2 x minus 3 right parenthesis end cell equals cell 4 x minus 6 minus 3 end cell row cell g left parenthesis 2 x minus 3 right parenthesis end cell equals cell 2 left parenthesis 2 x minus 3 right parenthesis minus 3 end cell row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 3 end cell end table 

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 3 end cell row y equals cell 2 x minus 3 end cell row cell 2 x end cell equals cell y plus 3 end cell row x equals cell fraction numerator y plus 3 over denominator 2 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 3 over denominator 2 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis 3 right parenthesis end cell equals cell fraction numerator 3 plus 3 over denominator 2 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis 3 right parenthesis end cell equals 3 end table 

Jadi, nilai dari g to the power of negative 1 end exponent left parenthesis 3 right parenthesis equals 3  

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Sutiawan

Mahasiswa/Alumni Universitas Pasundan

Terakhir diupdate 02 Mei 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pembahasan Soal:

Diketahui open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 10 x squared minus 8 x minus 3 dan g open parentheses x close parentheses equals 2 x plus 4 maka:

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 f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row cell 10 x squared minus 8 x minus 3 end cell equals cell f left parenthesis 2 x plus 4 right parenthesis end cell row cell misal space 2 x plus 4 end cell equals cell y comma space maka space x equals fraction numerator y minus 4 over denominator 2 end fraction end cell row cell 10 open parentheses fraction numerator y minus 4 over denominator 2 end fraction close parentheses squared minus 8 open parentheses fraction numerator y minus 4 over denominator 2 end fraction close parentheses minus 3 end cell equals cell f open parentheses 2 open parentheses fraction numerator y minus 4 over denominator 2 end fraction close parentheses plus 4 close parentheses end cell row cell 10 open parentheses fraction numerator y squared minus 8 y plus 16 over denominator 4 end fraction close parentheses minus 4 y plus 16 minus 3 end cell equals cell f left parenthesis y right parenthesis end cell row cell fraction numerator 10 y squared over denominator 4 end fraction minus fraction numerator 80 y over denominator 4 end fraction plus 160 over 4 minus 4 y plus 13 end cell equals cell f left parenthesis y right parenthesis end cell row cell 5 over 2 y squared minus 20 y plus 40 minus 4 y plus 13 end cell equals cell f left parenthesis y right parenthesis end cell row cell 5 over 2 y squared minus 24 y plus 53 end cell equals cell f left parenthesis y right parenthesis end cell row cell f left parenthesis x right parenthesis end cell equals cell 5 over 2 x squared minus 24 x plus 53 end cell end table 

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 5 over 2 x squared minus 24 x plus 53 end cell row y equals cell 5 over 2 x squared minus 24 x plus 53 end cell row cell 2 y end cell equals cell 5 x squared minus 48 x plus 106 end cell end table

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table attributes columnalign right center left columnspacing 0px end attributes row x equals cell fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction end cell row blank equals cell fraction numerator negative left parenthesis negative 48 right parenthesis plus-or-minus square root of left parenthesis negative 48 right parenthesis squared minus 4 left parenthesis 5 right parenthesis left parenthesis 106 minus 2 y right parenthesis end root over denominator 2 left parenthesis 5 right parenthesis end fraction end cell row blank equals cell fraction numerator 48 plus-or-minus square root of 2.304 minus 2.120 plus 40 y end root over denominator 10 end fraction end cell row blank equals cell fraction numerator 48 plus-or-minus square root of 40 y plus 184 end root over denominator 10 end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 24 plus-or-minus square root of 10 y plus 46 end root right parenthesis over denominator 10 end fraction end cell row blank equals cell fraction numerator left parenthesis 24 plus-or-minus square root of 10 y plus 46 end root right parenthesis over denominator 5 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator left parenthesis 24 plus-or-minus square root of 10 x plus 46 end root right parenthesis over denominator 5 end fraction end cell end table 

Jadi jawabannya tidak ada pada opsi, jawaban yang benar adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f to the power of negative 1 end exponent left parenthesis 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 cell fraction numerator left parenthesis 24 plus-or-minus square root of 10 x plus 46 end root right parenthesis over denominator 5 end fraction end cell end table 

0

Roboguru

Diketahui . Nilai dari

Pembahasan Soal:

Diketahui f open parentheses x close parentheses equals 2 x minus 3 space dan space open parentheses g ring operator f close parentheses open parentheses x close parentheses equals 4 x minus 9, maka g open parentheses x close parentheses didapatkan:

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 4 x minus 9 end cell row cell g open parentheses f open parentheses x close parentheses close parentheses end cell equals cell 4 x minus 9 end cell row cell g open parentheses 2 x minus 3 close parentheses end cell equals cell 4 x minus 9 end cell row cell g open parentheses x close parentheses end cell equals cell 4 open parentheses fraction numerator x plus 3 over denominator 2 end fraction close parentheses minus 9 end cell row cell g open parentheses x close parentheses end cell equals cell 2 open parentheses x plus 3 close parentheses minus 9 end cell row cell g open parentheses x close parentheses end cell equals cell 2 x plus 6 minus 9 end cell row cell g open parentheses x close parentheses end cell equals cell 2 x minus 3 end cell end table 

Fungsi g to the power of negative 1 end exponent open parentheses x close parentheses didapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 x minus 3 end cell row cell 2 x end cell equals cell y plus 3 end cell row x equals cell fraction numerator y plus 3 over denominator 2 end fraction end cell row blank blank blank row cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x plus 3 over denominator 2 end fraction end cell end table 

Nilai dari g to the power of negative 1 end exponent open parentheses 3 close parentheses diapatkan:

table attributes columnalign right center left columnspacing 0px end attributes row cell g to the power of negative 1 end exponent open parentheses 3 close parentheses end cell equals cell fraction numerator 3 plus 3 over denominator 2 end fraction end cell row blank equals cell 6 over 2 end cell row blank equals 3 end table 

Jadi, nilai dari g to the power of negative 1 end exponent open parentheses 3 close parentheses equals 3

0

Roboguru

Diketahui fungsi . Invers fungsi  adalah ....

Pembahasan Soal:

Diketahui begin mathsize 14px style f left parenthesis x minus 2 right parenthesis equals fraction numerator x over denominator 2 x minus 1 end fraction end style, misalkan begin mathsize 14px style x minus 2 equals y end style maka begin mathsize 14px style x equals y plus 2 end style. Sehingga:

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Misalkan begin mathsize 14px style f open parentheses x close parentheses equals y end style maka begin mathsize 14px style x equals f to the power of negative 1 end exponent open parentheses y close parentheses end style sehingga:

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator x plus 2 over denominator 2 x minus 3 end fraction end cell row y equals cell fraction numerator x plus 2 over denominator 2 x minus 3 end fraction end cell row cell 2 x y minus 3 y end cell equals cell x plus 2 end cell row cell negative 3 y minus 2 end cell equals cell x open parentheses 1 minus 2 y close parentheses end cell row x equals cell fraction numerator negative 3 y minus 2 over denominator 1 minus 2 y end fraction end cell row cell f to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator negative 3 y minus 2 over denominator 1 minus 2 y end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 3 x minus 2 over denominator 1 minus 2 x end fraction end cell row blank blank blank end table end style 

Jadi, invers fungsi begin mathsize 14px style f open parentheses x close parentheses end style adalah begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator negative 3 x minus 2 over denominator 1 minus 2 x end fraction end cell end table end style.

0

Roboguru

Jika diketahui fungsi  dan  dengan  dan , maka  adalah ...

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell 12 x minus 7 end cell row cell g open parentheses f left parenthesis x right parenthesis close parentheses end cell equals cell 12 x minus 7 end cell row cell g open parentheses 3 x minus 6 close parentheses end cell equals cell 12 x minus 7 end cell end table


Untuk mencari g left parenthesis x right parenthesis, kita misalkan y equals 3 x minus 6 dan substitusikan x equals fraction numerator y plus 6 over denominator 3 end fraction.


table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis y right parenthesis end cell equals cell 12 open parentheses fraction numerator y plus 6 over denominator 3 end fraction close parentheses minus 7 end cell row blank equals cell 4 open parentheses y plus 6 close parentheses minus 7 end cell row blank equals cell 4 y plus 24 minus 7 end cell row blank equals cell 4 y plus 17 end cell row cell g left parenthesis x right parenthesis end cell equals cell 4 x plus 17 end cell end table


table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell 4 x plus 17 end cell row cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x minus 17 over denominator 4 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis 5 right parenthesis end cell equals cell fraction numerator 5 minus 17 over denominator 4 end fraction end cell row blank equals cell fraction numerator negative 12 over denominator 4 end fraction end cell row blank equals cell negative 3 end cell end table


Jadi g to the power of negative 1 end exponent left parenthesis 5 right parenthesis equals negative 3.

0

Roboguru

Jika diketahui  dan fungsi , maka ....

Pembahasan Soal:

Diketahui left parenthesis f o g right parenthesis left parenthesis x right parenthesis space equals space 4 x ² minus 6 x plus 5 dan fungsi italic g left parenthesis italic x right parenthesis equals space 2 italic x minus sign 3 Dengan demikian diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f o g right parenthesis left parenthesis x right parenthesis space end cell equals cell space 4 x ² minus 6 x plus 5 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 4 x ² minus 6 x plus 5 end cell end table

Misalkan italic g left parenthesis italic x right parenthesis equals y, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell space 2 italic x minus sign 3 end cell row cell 2 x end cell equals cell y plus 3 end cell row x equals cell fraction numerator y plus 3 over denominator 2 end fraction end cell end table

Oleh karena itu,

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses y close parentheses end cell equals cell 4 open parentheses fraction numerator y plus 3 over denominator 2 end fraction close parentheses 2 minus 6 open parentheses fraction numerator y plus 3 over denominator 2 end fraction close parentheses plus 5 end cell row blank equals cell y squared plus 6 y plus 9 minus 3 y plus 5 end cell row blank equals cell y squared plus 3 y plus 5 end cell end table

Untuk y equals x, 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 plus 3 x plus 5 end cell end table.

Jadi, diperoleh nilai dari f left parenthesis x right parenthesis equals x squared plus 3 x plus 5.

0

Roboguru

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