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, invers fungsi f adalah ....

Pertanyaan

f open parentheses x close parentheses equals fraction numerator 3 x minus 1 over denominator 2 end fraction plus 4 x, invers fungsi f adalah ....

Pembahasan Soal:

Sebelum fungsi tersebut diinverskan, terlebih dahulu fungsi tersebut disederhanakan seperti berikut.

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell fraction numerator 3 x minus 1 over denominator 2 end fraction plus 4 x end cell row blank equals cell fraction numerator 3 x minus 1 over denominator 2 end fraction plus fraction numerator 8 x over denominator 2 end fraction end cell row blank equals cell fraction numerator 3 x minus 1 plus 8 x over denominator 2 end fraction end cell row blank equals cell fraction numerator 11 x minus 1 over denominator 2 end fraction end cell end table 

Selanjutnya, dapat dilakukan invers pada fungs rasional tersebut.

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell f open parentheses x close parentheses end cell row y equals cell fraction numerator 11 x minus 1 over denominator 2 end fraction end cell row cell 2 y end cell equals cell 11 x minus 1 end cell row cell 11 x end cell equals cell 2 y plus 1 end cell row x equals cell fraction numerator 2 y plus 1 over denominator 11 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 2 y plus 1 over denominator 11 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 2 x plus 1 over denominator 11 end fraction end cell end table 

Dengan demikian, invers fungsi f adalah f open parentheses x close parentheses equals fraction numerator 3 x minus 1 over denominator 2 end fraction plus 4 x rightwards arrow f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 2 x plus 1 over denominator 11 end fraction.

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

P. Tessalonika

Mahasiswa/Alumni Universitas Negeri Medan

Terakhir diupdate 07 Juni 2021

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Pertanyaan yang serupa

Jika  maka

Pembahasan Soal:

Diketahui f left parenthesis x right parenthesis equals fraction numerator negative 2 x plus 4 over denominator x minus 6 end fraction semicolon x not equal to 6 maka f to the power of negative 1 end exponent open parentheses x close parentheses sebagai berikut.

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

Kemudian, f to the power of negative 1 end exponent open parentheses x close parentheses di atas terdefinisi saat x plus 2 not equal to 0x plus 2 not equal to 0maka x not equal to negative 2. Oleh karena itu, f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 6 x plus 4 over denominator x plus 2 end fraction dengan x not equal to negative 2


Jadi, jawaban yang benar adalah E.

0

Roboguru

Tentukan fungsi invers dari fungsi sebagai berikut: 3)

Pembahasan Soal:

Bentuk umum fungsi invers dari fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator a x plus b over denominator c x plus d end fraction end style adalah begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative d x plus b over denominator c x minus a end fraction end style.

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 5 minus 2 x over denominator 4 x plus 7 end fraction end style, dengan nilai begin mathsize 14px style a equals 5 comma space b equals negative 2 comma space c equals 4 comma space dan space d equals 7 end style.

Dengan demikian, fungsi inversnya adalah

begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative 7 x minus 2 over denominator 4 x minus 5 end fraction end style.

0

Roboguru

Daerah . Invers dari fungsi  adalah...

Pembahasan Soal:

Untuk menentukan invers fungsi, maka fungsi rasional tersebut diubah ke bentuk sebagai berikut:

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

Sehingga, f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator negative 4 x plus 3 over denominator 5 x minus 2 end fraction dan fungsi invers di atas tidak terdefinisi saat:

table attributes columnalign right center left columnspacing 0px end attributes row cell 5 x minus 2 end cell equals 0 row cell 5 x end cell equals 2 row x equals cell 2 over 5 end cell end table 

Oleh karena itu, jawaban yang benar adalah D.

0

Roboguru

Jika fungsi  dan g(x) = 3x + 1 maka = ....

Pembahasan Soal:

begin mathsize 14px style straight i right parenthesis space Cari space straight g ring operator straight f  space space space open parentheses straight g ring operator straight f close parentheses open parentheses straight x close parentheses equals straight g open parentheses straight f open parentheses straight x close parentheses close parentheses equals 3 straight f open parentheses straight x close parentheses plus 1 equals 3. fraction numerator 2 straight x plus 3 over denominator straight x minus 5 end fraction plus 1 equals fraction numerator 6 straight x plus 9 over denominator straight x minus 5 end fraction plus fraction numerator straight x minus 5 over denominator straight x minus 5 end fraction  space space space equals fraction numerator 6 straight x plus 9 plus straight x minus 5 over denominator straight x minus 5 end fraction equals fraction numerator 7 straight x plus 4 over denominator straight x minus 5 end fraction    ii right parenthesis space Cari space invers space dengan space formula space berikut  space space space space straight h open parentheses straight x close parentheses equals fraction numerator ax plus straight b over denominator cx plus straight d end fraction rightwards arrow straight h to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator negative dx plus straight b over denominator cx minus straight a end fraction    space space space space open parentheses straight g ring operator straight f close parentheses open parentheses straight x close parentheses equals fraction numerator 7 straight x plus 4 over denominator straight x minus 5 end fraction  space space space space Dengan space straight a equals 7 comma space straight b equals 4 comma space straight c equals 1 comma space straight d equals negative 5 comma space maka  space space space space open parentheses straight g ring operator straight f close parentheses to the power of negative 1 end exponent open parentheses straight x close parentheses equals fraction numerator 5 straight x plus 4 over denominator straight x minus 7 end fraction end style

0

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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Roboguru

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