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Diketahui fungsi dan adalah invers . Jika k adalah...

Diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator x plus 1 over denominator x end fraction comma space x not equal to 0 end style dan begin mathsize 14px style f to the power of negative 1 end exponent end style adalah invers begin mathsize 14px style f end style. Jika k adalah banyaknya faktor prima dari 210, maka begin mathsize 14px style f to the power of negative 1 end exponent open parentheses k close parentheses equals... end style

  1. begin mathsize 14px style bevelled 1 fifth end style

  2. begin mathsize 14px style bevelled 1 fourth end style

  3. begin mathsize 14px style bevelled 1 third end style

  4. begin mathsize 14px style 3 end style

  5. begin mathsize 14px style 4 end style

Jawaban:

Pertama kita tentukan 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 x plus 1 over denominator x end fraction end cell row y equals cell fraction numerator x plus 1 over denominator x end fraction end cell row cell x y end cell equals cell x plus 1 end cell row cell x y minus x end cell equals 1 row cell x left parenthesis y minus 1 right parenthesis end cell equals 1 row x equals cell fraction numerator 1 over denominator left parenthesis y minus 1 right parenthesis end fraction end cell row blank blank cell f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 1 over denominator left parenthesis x minus 1 right parenthesis end fraction end cell end table end style

selanjunya kita menetukan nilai k dimana k adalah faktor prima dari 210:

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell faktor space prima space dari space 120 end cell equals cell open curly brackets 2 comma space 3 comma space 5 comma space dan space 7 close curly brackets end cell row straight k equals 4 end table end style   

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell size 14px f to the power of size 14px minus size 14px 1 end exponent begin mathsize 14px style left parenthesis x right parenthesis end style end cell size 14px equals cell fraction numerator size 14px 1 over denominator size 14px x size 14px minus size 14px 1 end fraction end cell row cell size 14px f to the power of size 14px minus size 14px 1 end exponent begin mathsize 14px style left parenthesis 4 right parenthesis end style end cell size 14px equals cell fraction numerator size 14px 1 over denominator size 14px 4 size 14px minus size 14px 1 end fraction end cell row cell size 14px f to the power of size 14px minus size 14px 1 end exponent begin mathsize 14px style left parenthesis 4 right parenthesis end style end cell size 14px equals cell size 14px 1 over size 14px 3 end cell row blank blank blank end table

Jadi, jawaban yang tepat adalah C

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