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Pertanyaan

Jika begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator x plus 3 over denominator x minus 2 end fraction end style, maka undefined

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator x plus 3 over denominator x minus 2 end fraction end cell row cell y times left parenthesis x minus 2 right parenthesis end cell equals cell x plus 3 end cell row cell x y minus 2 y end cell equals cell x plus 3 end cell row cell x y minus x end cell equals cell 3 plus 2 y end cell row cell x times left parenthesis y minus 1 right parenthesis end cell equals cell 3 plus 2 y end cell row x equals cell fraction numerator 3 plus 2 y over denominator y minus 1 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 3 plus 2 x over denominator x minus 1 end fraction end cell end table end style 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

A. Acfreelance

Terakhir diupdate 30 Maret 2021

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Pertanyaan yang serupa

Jika , maka tentukan .

Pembahasan Soal:

Menentukan f to the power of negative 1 end exponent left parenthesis x right parenthesis

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x minus 5 over denominator x minus 9 end fraction end cell row y equals cell fraction numerator 2 x minus 5 over denominator x minus 9 end fraction end cell row cell y left parenthesis x minus 9 right parenthesis end cell equals cell 2 x minus 5 end cell row cell x y minus 9 y end cell equals cell 2 x minus 5 end cell row cell x y minus 2 x end cell equals cell 9 y minus 5 end cell row cell x left parenthesis y minus 2 right parenthesis end cell equals cell 9 y minus 5 end cell row x equals cell fraction numerator 9 y minus 5 over denominator y minus 2 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator 9 y minus 5 over denominator y minus 2 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 9 x minus 5 over denominator x minus 2 end fraction end cell end table 

f to the power of negative 1 end exponent left parenthesis x right parenthesis akan memiliki nilai jika penyebutnya tidak sama dengan nol, sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell x minus 2 end cell not equal to 0 row x not equal to 2 end table 

Jadi, invers dari f left parenthesis x right parenthesis adalah f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 9 x minus 5 over denominator x minus 2 end fraction comma space x not equal to 2.

1

Roboguru

Jika  adalah invers dari , maka nilai

Pembahasan Soal:

Jika begin mathsize 14px style g to the power of negative 1 end exponent end style adalah invers dari begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 8 minus 3 x over denominator 4 minus x end fraction comma space x not equal to 4 end style, maka nilai begin mathsize 14px style g to the power of negative 1 end exponent open parentheses 4 close parentheses equals... end style 

begin mathsize 14px style g open parentheses x close parentheses equals fraction numerator 8 minus 3 x over denominator 4 minus x end fraction space space space space y equals fraction numerator 8 minus 3 x over denominator 4 minus x end fraction y open parentheses 4 minus x close parentheses equals 8 minus 3 x 4 y minus x y equals 8 minus 3 x 3 x minus x y equals 8 minus 4 y x open parentheses 3 minus y close parentheses equals 8 minus 4 y x equals fraction numerator 8 minus 4 y over denominator 3 minus y end fraction g to the power of negative 1 end exponent open parentheses y close parentheses equals fraction numerator 8 minus 4 y over denominator 3 minus y end fraction g to the power of negative 1 end exponent open parentheses 4 close parentheses equals fraction numerator 8 minus 4 open parentheses 4 close parentheses over denominator 3 minus 4 end fraction space space space space space space space space space space space space equals 8 end style 

 

1

Roboguru

Invers dari fungsi  adalah

Pembahasan Soal:

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 fraction numerator 2 x minus 7 over denominator 3 x plus 8 end fraction end cell row y equals cell fraction numerator 2 x minus 7 over denominator 3 x plus 8 end fraction end cell row cell 3 x y plus 8 y end cell equals cell 2 x minus 7 end cell row cell 3 x y minus 2 x end cell equals cell negative 8 y minus 7 end cell row cell x left parenthesis 3 y minus 2 right parenthesis end cell equals cell negative 8 y minus 7 end cell row x equals cell fraction numerator negative 8 y minus 7 over denominator 3 y minus 2 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 negative 8 x minus 7 over denominator 3 x minus 2 end fraction end cell end table end style

1

Roboguru

Jika , maka tentukan .

Pembahasan Soal:

misal space space fraction numerator 2 x minus 5 over denominator x minus 9 end fraction equals a space space space space space space space space space space space space 2 x minus 5 equals a open parentheses x minus 9 close parentheses space space space space space space space space space space space space 2 x minus 5 equals a x minus 9 a space space space space space space space space space 2 x minus a x equals negative 9 a plus 5 space space space space space space space space space open parentheses 2 minus a close parentheses x equals negative 9 a plus 5 space space space space space space space space space space space space space space space space space space space space x equals fraction numerator negative 9 a plus 5 over denominator 2 minus a end fraction space space space space space space space space space space space space space space space space space space space space x equals fraction numerator 9 a minus 5 over denominator a minus 2 end fraction 

Jadi, f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 9 x minus 5 over denominator x minus 2 end fraction comma space x not equal to 2.

1

Roboguru

Diketahui fungsi , , dan , . Jika  adalah fungsi invers dari , nilai  ....

Pembahasan Soal:

Pada soal diketahui:

f left parenthesis x right parenthesis equals 2 minus 3 x g left parenthesis x right parenthesis equals 4 x minus 5 h left parenthesis x right parenthesis equals fraction numerator f left parenthesis x right parenthesis over denominator g left parenthesis x right parenthesis end fraction h left parenthesis x right parenthesis equals fraction numerator 2 minus 3 x over denominator 4 x minus 5 end fraction space comma space x not equal to 5 over 4

Pertama kita tentukan fungsi invers h to the power of negative 1 end exponent open parentheses x close parentheses:

table attributes columnalign right center left columnspacing 0px end attributes row cell h open parentheses x close parentheses end cell equals cell fraction numerator 2 minus 3 x over denominator 4 x minus 5 end fraction end cell row y equals cell fraction numerator 2 minus 3 x over denominator 4 x minus 5 end fraction end cell row cell y left parenthesis 4 x minus 5 right parenthesis end cell equals cell 2 minus 3 x end cell row cell 4 x y minus 5 y end cell equals cell 2 minus 3 x end cell row cell 4 x y plus 3 x end cell equals cell 2 plus 5 y end cell row cell x left parenthesis 4 y plus 3 right parenthesis end cell equals cell 2 plus 5 y end cell row x equals cell fraction numerator 2 plus 5 y over denominator left parenthesis 4 y plus 3 right parenthesis end fraction end cell row cell h to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 2 plus 5 x over denominator left parenthesis 4 x plus 3 right parenthesis end fraction space comma space x not equal to negative 3 over 4 end cell end table

Sehingga nilai dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell h to the power of negative 1 end exponent left parenthesis 2 right parenthesis end cell end table adalah:

table attributes columnalign right center left columnspacing 0px end attributes row cell h to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 2 plus 5 x over denominator left parenthesis 4 x plus 3 right parenthesis end fraction space end cell row cell h to the power of negative 1 end exponent left parenthesis 2 right parenthesis end cell equals cell fraction numerator 2 plus 5 left parenthesis 2 right parenthesis over denominator left parenthesis 4 left parenthesis 2 right parenthesis plus 3 right parenthesis end fraction end cell row cell h to the power of negative 1 end exponent left parenthesis 2 right parenthesis end cell equals cell 12 over 11 end cell end table    

Jadi, nilai dari table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell h to the power of negative 1 end exponent left parenthesis 2 right parenthesis end cell end table adalah table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell 12 over 11 end cell end table

Jadi, jawaban yang tepat adalah D.undefined 

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