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Diketahui f(x)=5x−2x+7​,x=52​ maka f−1(x)=…

Pertanyaan

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator x plus 7 over denominator 5 x minus 2 end fraction comma space x not equal to 2 over 5 end style maka begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals horizontal ellipsis end style 

  1. begin mathsize 14px style fraction numerator 2 x plus 7 over denominator 5 x minus 1 end fraction comma space x not equal to 1 fifth end style 

  2. fraction numerator size 14px 5 size 14px x size 14px minus size 14px 2 over denominator size 14px x size 14px plus size 14px 7 end fraction size 14px comma size 14px space size 14px x size 14px not equal to size 14px minus size 14px 7 

  3. fraction numerator size 14px 7 size 14px x size 14px plus size 14px 1 over denominator size 14px minus size 14px 2 size 14px x size 14px plus size 14px 5 end fraction size 14px comma size 14px space size 14px x size 14px not equal to size 14px 5 over size 14px 2 

  4. begin mathsize 14px style fraction numerator x minus 2 over denominator 5 x plus 7 end fraction comma space x not equal to negative 7 over 5 end style 

  5. begin mathsize 14px style fraction numerator 2 x minus 7 over denominator 5 x plus 1 end fraction comma space x not equal to negative 1 fifth end style 

Pembahasan Soal:

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator x plus 7 over denominator 5 x minus 2 end fraction comma space x not equal to 2 over 5 end style

Bentuk umum invers 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 comma space x not equal to a over c end style.

Oleh karena itu,

begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator negative left parenthesis negative 2 right parenthesis x plus 7 over denominator 5 x minus 1 end fraction equals fraction numerator 2 x plus 7 over denominator 5 x minus 1 end fraction comma space x not equal to 1 fifth end style  

Dengan demikian, bentuk invers dari fungsi undefined adalah begin mathsize 14px style fraction numerator 2 x plus 7 over denominator 5 x minus 1 end fraction comma space x not equal to 1 fifth end style.

Jadi, jawaban yang tepat adalah A. 

Pembahasan terverifikasi oleh Roboguru

Dijawab oleh:

I. Kumaralalita

Mahasiswa/Alumni Universitas Gadjah Mada

Terakhir diupdate 05 Oktober 2021

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Pertanyaan yang serupa

Tentukan invers dari g(x)=x3​+7 ?

Pembahasan Soal:

Invers fungsi undefined sebagai berikut:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell equals cell 3 over x plus 7 end cell row y equals cell 3 over x plus 7 end cell row cell y minus 7 end cell equals cell 3 over x end cell row cell x open parentheses y minus 7 close parentheses end cell equals 3 row x equals cell fraction numerator 3 over denominator y minus 7 end fraction end cell end table end style 

Sehingga, begin mathsize 14px style g to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 3 over denominator x minus 7 end fraction end style.

0

Roboguru

Diketahui fungsi f(x)=2x+94x−5​,x=−29​. Invers fungsi dari f(x) adalah ...

Pembahasan Soal:

Diketahui:

f left parenthesis x right parenthesis equals fraction numerator 4 x minus 5 over denominator 2 x plus 9 end fraction comma space x not equal to negative 9 over 2

Mencari invers fungsi f 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 4 x minus 5 over denominator 2 x plus 9 end fraction comma space x not equal to negative 9 over 2 end cell row y equals cell fraction numerator 4 x minus 5 over denominator 2 x plus 9 end fraction end cell row x equals cell fraction numerator 4 y minus 5 over denominator 2 y plus 9 end fraction end cell row cell x left parenthesis 2 y plus 9 right parenthesis end cell equals cell 4 y minus 5 end cell row cell 2 x y plus 9 x end cell equals cell 4 y minus 5 end cell row cell 2 x y minus 4 y end cell equals cell negative 9 x minus 5 end cell row cell 2 y left parenthesis x minus 2 right parenthesis end cell equals cell negative 9 x minus 5 end cell row cell 2 y end cell equals cell fraction numerator negative 9 x minus 5 over denominator left parenthesis x minus 2 right parenthesis end fraction end cell row y equals cell fraction numerator negative 9 x minus 5 over denominator 2 left parenthesis x minus 2 right parenthesis end fraction end cell row y equals cell fraction numerator negative 9 x minus 5 over denominator 2 x minus 4 end fraction comma space x not equal to 2 end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell negative fraction numerator 9 x plus 5 over denominator 2 x minus 4 end fraction comma space x not equal to 2 end cell end table 

Jadi, invers fungsi f left parenthesis x right parenthesis equals fraction numerator 4 x minus 5 over denominator 2 x plus 9 end fraction comma space x not equal to negative 9 over 2 adalah f to the power of negative 1 end exponent equals negative fraction numerator 9 x plus 5 over denominator 2 x minus 4 end fraction comma space x not equal to 2.

Dengan demikian, jawaban yang tepat adalah C.

1

Roboguru

Diketahui fungsi f(x)=4x−72x​,x=47​. Invers fungsi dari f(x) adalah...

Pembahasan Soal:

Dengan menggunakan konsep invers fungsi rasional maka diperoleh

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals y row cell fraction numerator 2 x over denominator 4 x minus 7 end fraction end cell equals y row cell 2 x end cell equals cell y open parentheses 4 x minus 7 close parentheses end cell row cell 2 x end cell equals cell 4 x y minus 7 y end cell row cell 2 x minus 4 x y end cell equals cell negative 7 y end cell row cell x open parentheses 2 minus 4 y close parentheses end cell equals cell negative 7 y end cell row x equals cell fraction numerator negative 7 y over denominator 2 minus 4 y end fraction comma y not equal to 1 half end cell row x equals cell fraction numerator 7 y over denominator 4 y minus 2 end fraction comma y not equal to 1 half end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 7 x over denominator 4 x minus 2 end fraction comma x not equal to 1 half end cell end table

Dengan demikian invers fungsi dari f open parentheses x close parentheses adalah 

Error converting from MathML to accessible text..

Oleh karena itu, jawaban yang benar adalah B.

0

Roboguru

Diketahui fungsi f(x)=2x+94x−5​, x=−29​. lnvers fungsi dari f(x) adalah ....

Pembahasan Soal:

Diketahui: begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 4 x minus 5 over denominator 2 x plus 9 end fraction end stylebegin mathsize 14px style x not equal to negative 9 over 2 end style

misalkan : begin mathsize 14px style y equals f open parentheses x close parentheses end style

maka invers dari begin mathsize 14px style f open parentheses x close parentheses end style:

 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 4 x minus 5 over denominator 2 x plus 9 end fraction end cell row y equals cell fraction numerator 4 x minus 5 over denominator 2 x plus 9 end fraction end cell row cell 2 x y plus 9 y end cell equals cell 4 x minus 5 end cell row cell 9 y plus 5 end cell equals cell 4 x minus 2 x y end cell row cell 9 y plus 5 end cell equals cell x open parentheses 4 minus 2 y close parentheses end cell row cell fraction numerator 9 y plus 5 over denominator 4 minus 2 y end fraction end cell equals x row blank blank blank end table end style 

Oleh karena begin mathsize 14px style y equals f open parentheses x close parentheses 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 x equals cell fraction numerator 9 y plus 5 over denominator 4 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 9 x plus 5 over denominator 4 minus 2 x end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell negative fraction numerator 9 x plus 5 over denominator 2 x minus 4 end fraction comma space x not equal to 2 end cell end table end style  

Jadi, jawaban yang tepat adalah C. 

 

0

Roboguru

Jika f(x)=4x+52x−1​, maka f−1(x)=...

Pembahasan Soal:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row y equals cell fraction numerator 2 x minus 1 over denominator 4 x plus 5 end fraction end cell row cell y left parenthesis 4 x plus 5 right parenthesis end cell equals cell 2 x minus 1 end cell row cell 4 x y plus 5 y end cell equals cell 2 x minus 1 end cell row cell 4 x y minus 2 x end cell equals cell negative 5 y minus 1 end cell row cell x left parenthesis 4 y minus 2 right parenthesis end cell equals cell negative 5 y minus 1 end cell row x equals cell fraction numerator negative 5 y minus 1 over denominator 4 y minus 2 end fraction cross times fraction numerator negative 1 over denominator negative 1 end fraction end cell row x equals cell fraction numerator 5 y plus 1 over denominator 2 minus 4 y 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 5 x plus 1 over denominator 2 minus 4 x end fraction end cell end table end style

Jadi, jawaban yang tepat adalah A 

0

Roboguru

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