Diketahui: Sehingga dapat ditentukan sebagai berikut. Dengan demikian, diperoleh nilai .

Jika dan maka

Pertanyaan

Jika $f left parenthesis x right parenthesis equals 3 x plus 2$ dan $f open parentheses g open parentheses x close parentheses close parentheses equals 6 x minus 7$ maka $g open parentheses 4 close parentheses equals....$

Pembahasan Soal:

Diketahui:

$table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 3 x plus 2 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 6 x minus 7 end cell end table$

Sehingga dapat ditentukan $g open parentheses 4 close parentheses$ sebagai berikut.

$table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell 6 x minus 7 end cell row cell 3 times g open parentheses x close parentheses plus 2 end cell equals cell 6 x minus 7 end cell row cell 3 times g open parentheses x close parentheses end cell equals cell 6 x minus 9 end cell row cell g open parentheses x close parentheses end cell equals cell fraction numerator 6 x minus 9 over denominator 3 end fraction end cell row blank equals cell 2 x minus 3 end cell row cell g open parentheses 4 close parentheses end cell equals cell 2 times 4 minus 3 end cell row blank equals cell 8 minus 3 end cell row blank equals 5 end table$

Dengan demikian, diperoleh nilai $g open parentheses 4 close parentheses equals 5$ .

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

P. Afrisno

Mahasiswa/Alumni Universitas Sebelas Maret

Terakhir diupdate 07 Juni 2021

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Diketahui fungsi . Tentukan: a. Invers fungsi b. Nilai dari

Pembahasan Soal:

Diketahui fungsi $begin mathsize 14px style f left parenthesis x right parenthesis equals 4 x plus 2 space dan space left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals 8 x plus 3 end style$ .

Menentukan $begin mathsize 14px style g left parenthesis x right parenthesis end style$ .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end cell equals cell 8 x plus 3 end cell row cell g left parenthesis f left parenthesis x right parenthesis right parenthesis end cell equals cell 8 x plus 3 end cell row cell g left parenthesis 4 x plus 2 right parenthesis end cell equals cell 8 x plus 3 end cell row blank blank blank end table end style$

Misalkan $begin mathsize 14px style a equals 4 x plus 2 space end style$ maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell a minus 2 end cell equals cell 4 x end cell row cell fraction numerator a minus 2 over denominator 4 end fraction end cell equals x end table end style$

Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis a right parenthesis end cell equals cell 8 left parenthesis fraction numerator a minus 2 over denominator 4 end fraction right parenthesis plus 3 end cell row cell g left parenthesis a right parenthesis end cell equals cell 2 left parenthesis a minus 2 right parenthesis plus 3 end cell row cell g left parenthesis a right parenthesis end cell equals cell 2 a minus 4 plus 3 end cell row cell g left parenthesis a right parenthesis end cell equals cell 2 a minus 1 end cell row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 1 end cell end table end style$

Menentukan invers fungsi $begin mathsize 14px style g end style$

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 1 end cell row y equals cell 2 x minus 1 end cell row cell y plus 1 end cell equals cell 2 x end cell row cell fraction numerator y plus 1 over denominator 2 end fraction end cell equals x row cell fraction numerator y plus 1 over denominator 2 end fraction end cell equals cell g to the power of negative 1 end exponent left parenthesis y right parenthesis end cell row cell fraction numerator x plus 1 over denominator 2 end fraction end cell equals cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table end style$

a. Jadi, $begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x plus 1 over denominator 2 end fraction end style$ .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g to the power of negative 1 end exponent left parenthesis 7 right parenthesis end cell equals cell fraction numerator 7 plus 1 over denominator 2 end fraction end cell row blank equals cell 8 over 2 end cell row blank equals 4 end table end style$

b. Jadi, nilai dari $begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis 7 right parenthesis equals 4 end style$ .

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Fungsi dan ditentukan dengan dan , maka = ...

Pembahasan Soal:

Menentukan $g left parenthesis x right parenthesis$

$table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell fraction numerator x minus 3 over denominator 2 x end fraction end cell row cell g left parenthesis x right parenthesis to the power of negative 1 end exponent end cell equals cell fraction numerator x minus 3 over denominator 2 x end fraction end cell row cell fraction numerator 1 over denominator g left parenthesis x right parenthesis end fraction end cell equals cell fraction numerator x minus 3 over denominator 2 x end fraction end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x over denominator x minus 3 end fraction semicolon space x not equal to 3 end cell end table$

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

$table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator 2 x over denominator x minus 3 end fraction end cell row y equals cell fraction numerator 2 x over denominator x minus 3 end fraction end cell row cell y left parenthesis x minus 3 right parenthesis end cell equals cell 2 x end cell row cell x y minus 3 y end cell equals cell 2 x end cell row cell x y minus 2 x end cell equals cell 3 y end cell row cell x left parenthesis y minus 2 right parenthesis end cell equals y row x equals cell fraction numerator y over denominator y minus 2 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator y over denominator y minus 2 end fraction end cell row cell g to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator x over denominator x minus 2 end fraction comma space x not equal to 2 end cell end table$

Dengan demikian, diperoleh $g to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x over denominator x minus 2 end fraction comma space x not equal to 2$ .

Roboguru

Jika dan , maka nilai adalah ....

Pembahasan Soal:

Diberikan fungsi $f left parenthesis x right parenthesis equals x squared plus 1$ dan fungsi komposisi $left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals 4 x squared minus 12 x plus 10$ , fungsi $g left parenthesis x right parenthesis$ dapat dihitung seperti berikut :

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f left parenthesis g right parenthesis left parenthesis x right parenthesis end cell equals cell 4 x squared minus 12 x plus 10 end cell row cell left parenthesis g left parenthesis x right parenthesis right parenthesis squared plus 1 end cell equals cell 4 x squared minus 12 x plus 10 end cell row cell left parenthesis g left parenthesis x right parenthesis right parenthesis squared end cell equals cell 4 x squared minus 12 x plus 10 minus 1 end cell row cell left parenthesis g left parenthesis x right parenthesis right parenthesis squared end cell equals cell 4 x squared minus 12 x plus 9 end cell row cell left parenthesis g left parenthesis x right parenthesis right parenthesis squared end cell equals cell left parenthesis 2 x minus 3 right parenthesis squared end cell row cell g left parenthesis x right parenthesis end cell equals cell square root of left parenthesis 2 x minus 3 right parenthesis squared end root end cell row cell g left parenthesis x right parenthesis end cell equals cell 2 x minus 3 end cell end table$

Dengan demikian, fungsi $g left parenthesis x right parenthesis$ adalah $2 x minus 3$ .

Jadi, jawaban yang terbentuk adalah A.

Roboguru

Jika dan , maka ...

Pembahasan Soal:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row cell space 1 minus 5 left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell negative 4 minus 25 x space end cell row cell negative 5 left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell negative 1 minus 4 minus 25 x space end cell row cell negative 5 left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell negative 25 x minus 5 space end cell row cell left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 5 x plus 1 end cell row cell space g left parenthesis x plus 1 right parenthesis end cell equals cell 5 left parenthesis x plus 1 right parenthesis plus 1 end cell row blank equals cell 5 x plus 5 plus 1 end cell row blank equals cell 5 x plus 6 end cell end table end style$

Jadi, jawaban yang tepat adalah D.

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Diketahuisuatu fungsi dan komposisi . Maka fungsi

Pembahasan Soal:

Diketahui:

$begin mathsize 14px style f left parenthesis x right parenthesis equals 4 x minus 1 left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis equals 12 x plus 7 end style$

Ditanya: $begin mathsize 14px style g left parenthesis x right parenthesis end style$ ?

Jawab:

Fungsi komposisi $begin mathsize 14px style left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end style$ didapat dengan mensubtitusi $undefined$ ke fungsi $begin mathsize 14px style f left parenthesis x right parenthesis end style$ .

Jadi, fungsi $begin mathsize 14px style g left parenthesis x right parenthesis equals 3 x plus 2 end style$ .

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