Roboguru

Diketahui fungsi . Maka komposisi fungsi dari adalah ....

Pertanyaan

Diketahui fungsi straight f open parentheses straight x close parentheses equals 4 straight x minus 1 space dan space fungsi space straight g open parentheses straight x close parentheses equals 3 straight x minus 2. space jika space fungsi space straight h open parentheses straight x close parentheses equals straight x minus 2. Maka komposisi fungsi dari open parentheses straight h ring operator straight g ring operator straight f close parentheses open parentheses straight x close parentheses adalah ....

  1. 12 straight x plus 2

  2. 12 straight x minus 7

  3. 12 straight x plus 5

  4. 12 straight x minus 5

  5. 12 straight x plus 7

Pembahasan Soal:

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight g ring operator straight f right parenthesis open parentheses straight x close parentheses end cell equals cell straight g open parentheses straight f open parentheses straight x close parentheses close parentheses end cell row blank equals cell 3 open parentheses 4 straight x minus 1 close parentheses minus 2 end cell row blank equals cell 12 straight x minus 3 minus 2 end cell row blank equals cell 12 straight x minus 5 end cell row cell open parentheses straight h ring operator straight g ring operator straight f close parentheses open parentheses straight x close parentheses end cell equals cell straight h open parentheses straight g open parentheses straight x close parentheses close parentheses end cell row blank equals cell open parentheses 12 straight x minus 5 close parentheses minus 2 end cell row blank equals cell 12 straight x minus 7 end cell end table

Oleh karena itu jawabannya adalah B

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Mahasiswa/Alumni UIN Walisongo Semarang

Terakhir diupdate 05 Juni 2021

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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Pertanyaan yang serupa

Diketahui  dan , fungsi  ...

Pembahasan Soal:

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 g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses 3 x minus 2 close parentheses end cell row blank equals cell fraction numerator 3 over denominator 3 x minus 2 plus 4 end fraction end cell row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell fraction numerator 3 over denominator 3 x plus 2 end fraction end cell end table end style 

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 y row y equals cell fraction numerator 3 over denominator 3 x plus 2 end fraction end cell row cell 3 x y plus 2 y end cell equals 3 row cell 3 x y end cell equals cell negative 2 y plus 3 end cell row x equals cell fraction numerator negative 2 y plus 3 over denominator 3 y end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 2 x plus 3 over denominator 3 x end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x plus 3 close parentheses end cell equals cell fraction numerator negative 2 open parentheses x plus 3 close parentheses plus 3 over denominator 3 open parentheses x plus 3 close parentheses end fraction end cell row blank equals cell fraction numerator negative 2 x minus 6 plus 3 over denominator 3 x plus 9 end fraction end cell row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x plus 3 close parentheses end cell equals cell fraction numerator negative 2 x minus 3 over denominator 3 x plus 9 end fraction end cell end table end style 

Jadi, jawaban yang tepat adalah E.
 

1

Roboguru

Diketahui fungsi   dan  Nilai   adalah ...

Pembahasan Soal:

Pertama akan dicari invers dari fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x minus 5 end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 x minus 5 end cell row cell 2 x end cell equals cell y plus 5 end cell row x equals cell fraction numerator y plus 5 over denominator 2 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 x plus 5 over denominator 2 end fraction end cell end table end style    

Dengan menggunakan sifat invers akan ditentukan begin mathsize 14px style left parenthesis f ring operator open parentheses g ring operator h close parentheses right parenthesis to the power of negative 1 end exponent 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 open parentheses g ring operator h close parentheses close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell h to the power of negative 1 end exponent open parentheses open parentheses g to the power of negative 1 end exponent open parentheses open parentheses f to the power of equals 1 end exponent open parentheses x close parentheses close parentheses close parentheses close parentheses close parentheses end cell row cell space space space space space space space space space space space space space space space space end cell equals cell h to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses fraction numerator x plus 5 over denominator 2 end fraction close parentheses close parentheses end cell row cell space space space space space space space space space space space space space space space space end cell equals cell h to the power of negative 1 end exponent open parentheses fraction numerator fraction numerator x plus 5 over denominator 2 end fraction plus 3 over denominator 4 end fraction close parentheses end cell row blank equals cell h to the power of negative 1 end exponent open parentheses fraction numerator begin display style fraction numerator x plus 5 plus 6 over denominator 2 end fraction end style over denominator 4 end fraction close parentheses end cell row blank equals cell h to the power of negative 1 end exponent open parentheses fraction numerator x plus 11 over denominator 8 end fraction close parentheses end cell row blank equals cell 8 open parentheses fraction numerator x plus 11 over denominator 8 end fraction close parentheses plus 1 end cell row blank equals cell x plus 11 plus 1 end cell row blank equals cell x plus 12 end cell end table end style       

Nilai fugsi  adalah begin mathsize 14px style left parenthesis f ring operator open parentheses g ring operator h close parentheses right parenthesis to the power of negative 1 end exponent open parentheses negative 7 close parentheses end style 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator left parenthesis g ring operator h right parenthesis right parenthesis to the power of negative 1 end exponent left parenthesis negative 7 right parenthesis end cell equals cell open parentheses negative 7 close parentheses plus 12 end cell row blank equals 5 end table end style 

 Jadi,nilai fungsi begin mathsize 14px style left parenthesis f ring operator open parentheses g ring operator h close parentheses right parenthesis to the power of negative 1 end exponent open parentheses negative 7 close parentheses end style adalah 5

0

Roboguru

Jika , , dan , maka

Pembahasan Soal:

Jika f open parentheses x close parentheses equals x plus 1g open parentheses x close parentheses equals x squared, dan h open parentheses x close parentheses equals fraction numerator x over denominator x minus 2 end fraction, maka

 table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses end cell equals cell h open parentheses f open parentheses g open parentheses x close parentheses close parentheses close parentheses end cell row blank equals cell h open parentheses f open parentheses x squared close parentheses close parentheses end cell row blank equals cell h open parentheses x squared plus 1 close parentheses end cell row blank equals cell fraction numerator x squared plus 1 over denominator x squared plus 1 minus 2 end fraction end cell row blank equals cell fraction numerator x squared plus 1 over denominator x squared minus 1 end fraction end cell end table

Jadi, open parentheses h ring operator f ring operator g close parentheses open parentheses x close parentheses equalsfraction numerator italic x squared plus 1 over denominator italic x squared minus sign 1 end fraction.

0

Roboguru

Jika ,  dan , nilai

Pembahasan Soal:

Menentukan begin mathsize 14px style left parenthesis g ring operator h right parenthesis left parenthesis x right parenthesis end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator h close parentheses open parentheses x close parentheses end cell equals cell g open parentheses h open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses x squared plus 4 x minus 3 close parentheses end cell row blank equals cell 3 open parentheses x squared plus 4 x minus 3 close parentheses plus 1 end cell row blank equals cell 3 x squared plus 12 x minus 9 plus 1 end cell row blank equals cell 3 x squared plus 12 x minus 8 end cell end table end style 

Menentukan begin mathsize 14px style left parenthesis g ring operator h ring operator f right parenthesis open parentheses x close parentheses end style.

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator h ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell left parenthesis open parentheses g ring operator h close parentheses ring operator f right parenthesis left parenthesis x right parenthesis end cell row blank equals cell 3 open parentheses x minus 2 close parentheses squared plus 12 left parenthesis x minus 2 right parenthesis minus 8 end cell row blank equals cell 3 open parentheses x squared minus 4 x plus 4 close parentheses plus 12 x minus 24 minus 8 end cell row blank equals cell 3 x squared minus up diagonal strike 12 x end strike plus 12 plus up diagonal strike 12 x end strike minus 32 end cell row blank equals cell 3 x squared minus 20 end cell end table end style 

Menentukan begin mathsize 14px style left parenthesis g ring operator h ring operator f right parenthesis left parenthesis 3 right parenthesis end style.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator h ring operator f right parenthesis left parenthesis 3 right parenthesis end cell equals cell 3 times open parentheses 3 close parentheses squared minus 20 end cell row blank equals cell 27 minus 20 end cell row blank equals 7 end table end style 

Jadi, jawaban yang tepat adalah E.

0

Roboguru

1. Diketahui fungsi  dengan  Tentukan: a.

Pembahasan Soal:

Perhatikan penghitungan berikut!

 begin mathsize 14px style left parenthesis h ring operator f ring operator g right parenthesis left parenthesis x right parenthesis equals h left parenthesis f left parenthesis g left parenthesis x right parenthesis right parenthesis left parenthesis h ring operator f ring operator g right parenthesis left parenthesis x right parenthesis equals h left parenthesis f left parenthesis 3 x minus 1 right parenthesis left parenthesis h ring operator f ring operator g right parenthesis left parenthesis x right parenthesis equals h left parenthesis left parenthesis 3 x minus 1 right parenthesis plus 2 right parenthesis left parenthesis h ring operator f ring operator g right parenthesis left parenthesis x right parenthesis equals h left parenthesis 3 x plus 1 right parenthesis left parenthesis h ring operator f ring operator g right parenthesis left parenthesis x right parenthesis equals left parenthesis 3 x plus 1 right parenthesis squared minus 1 space left parenthesis h ring operator f ring operator g right parenthesis left parenthesis x right parenthesis equals left parenthesis 9 x squared plus 6 x plus 1 right parenthesis minus 1 left parenthesis h ring operator f ring operator g right parenthesis left parenthesis x right parenthesis equals 9 x squared plus 6 x end style   

Jadi, fungsi begin mathsize 14px style open parentheses h ring operator f ring operator g close parentheses left parenthesis x right parenthesis equals 9 x squared plus 6 x. end style 

0

Roboguru

Roboguru sudah bisa jawab 91.4% pertanyaan dengan benar

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

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