Diketahui f(x)=2x−1, g(x)=3−x dan h(x)=x4​, x=0, tentukan nilai x sehingga (h∘g∘f)−1(x)=1.

Pertanyaan

Diketahui begin mathsize 14px style straight f left parenthesis x right parenthesis equals 2 x minus 1 end stylebegin mathsize 14px style straight g left parenthesis x right parenthesis equals 3 minus x end style dan begin mathsize 14px style straight h left parenthesis x right parenthesis equals 4 over x comma space x not equal to 0 end style, tentukan nilai x sehingga begin mathsize 14px style open parentheses straight h ring operator straight g ring operator straight f close parentheses to the power of negative 1 end exponent open parentheses x close parentheses equals 1 end style.

T. Rizki

Master Teacher

Jawaban terverifikasi

Jawaban

 nilai x sehingga bold left parenthesis bold italic h bold ring operator bold italic g bold ring operator bold italic f bold right parenthesis to the power of bold minus bold 1 end exponent bold left parenthesis bold italic x bold right parenthesis bold equals bold 1 adalah bold 1 over bold 2 bold.  

Pembahasan

Perhatikan perhitungan berikut 

table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses h ring operator g ring operator f close parentheses left parenthesis x right parenthesis end cell equals cell h open parentheses g open parentheses f open parentheses x close parentheses close parentheses close parentheses end cell row blank equals cell h open parentheses g open parentheses 2 x minus 1 close parentheses close parentheses end cell row blank equals cell h open parentheses 3 minus left parenthesis 2 x minus 1 right parenthesis close parentheses end cell row blank equals cell h open parentheses 4 minus 2 x close parentheses end cell end table

Lebih lanjut, diperoleh    

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

sehingga

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis h ring operator g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell negative 2 x plus 2 end cell row 1 equals cell negative 2 x plus 2 end cell row cell negative 1 end cell equals cell negative 2 x end cell row x equals cell 1 half end cell end table

Dengan demikian, nilai x sehingga bold left parenthesis bold italic h bold ring operator bold italic g bold ring operator bold italic f bold right parenthesis to the power of bold minus bold 1 end exponent bold left parenthesis bold italic x bold right parenthesis bold equals bold 1 adalah bold 1 over bold 2 bold.  

93

4.3 (6 rating)

Rama

Ini yang aku cari!

Maryam

Jawaban tidak sesuai Bagaimana sih caranya, ? ,, padahal sudah tak kirim foto soalnya

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