Diketahui f: R→R dan g: R→R dengan f(x)=x+2 dan g(x)=4−2x. Tentukan (g∘f)−1(x)!

Pertanyaan

Diketahui begin mathsize 14px style f colon space R rightwards arrow R space dan space g colon space R rightwards arrow R end style dengan begin mathsize 14px style f open parentheses x close parentheses equals x plus 2 end style dan begin mathsize 14px style g open parentheses x close parentheses equals 4 minus 2 x end style. Tentukan begin mathsize 14px style open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses end style!

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x over 2 end cell end table end style 

Pembahasan

Menentukan fungsi komposisi.

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses open parentheses x close parentheses end cell equals cell g open parentheses f open parentheses x close parentheses close parentheses end cell row blank equals cell g open parentheses x plus 2 close parentheses end cell row blank equals cell 4 minus 2 open parentheses x plus 2 close parentheses end cell row blank equals cell 4 minus 2 x minus 4 end cell row blank equals cell negative 2 x end cell end table end style 

Menentukan invers fungsi komposisi.

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 y row cell negative 2 x end cell equals y row x equals cell negative y over 2 end cell row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell negative y over 2 end cell row cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell negative x over 2 end cell end table end style  

Jadi, begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank minus end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell x over 2 end cell end table end style 

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Diketahui fungsi f(x)=2x−1, dan (g∘f)(x)=2x−3.  Tentukan: b.  (g∘f)−1(x)

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Jawaban terverifikasi

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