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Diketahui fungsi f(2x1​)=x+4 dan g(x)=x−3x+1​, x=3. Rumus komposisi fungsi (g∘f)(x) adalah ....

Pertanyaan

Diketahui fungsi begin mathsize 14px style f open parentheses fraction numerator 1 over denominator 2 x end fraction close parentheses equals x plus 4 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator x plus 1 over denominator x minus 3 end fraction end stylebegin mathsize 14px style x not equal to 3 end style. Rumus komposisi fungsi begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end style adalah ....

S. Amamah

Master Teacher

Mahasiswa/Alumni Universitas Negeri Malang

Jawaban terverifikasi

Jawaban

 begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 10 x plus 1 over denominator 2 x plus 1 end fraction end style.

Pembahasan

Diketahui begin mathsize 14px style f open parentheses fraction numerator 1 over denominator 2 x end fraction close parentheses equals x plus 4 end style, misalkan begin mathsize 14px style y equals fraction numerator 1 over denominator 2 x end fraction end style maka diperoleh begin mathsize 14px style x equals fraction numerator 1 over denominator 2 y end fraction end style sehingga 

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses y close parentheses end cell equals cell fraction numerator 1 over denominator 2 y end fraction plus 4 end cell row blank equals cell fraction numerator 1 plus 8 y over denominator 2 y end fraction end cell row cell f open parentheses x close parentheses end cell equals cell fraction numerator 1 plus 8 x over denominator 2 x end fraction end cell row blank blank blank end table end style  

dengan demikian komposisi fungsi begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis end style adalah

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 fraction numerator 1 plus 8 x over denominator 2 x end fraction close parentheses end cell row blank equals cell fraction numerator open parentheses fraction numerator 1 plus 8 x over denominator 2 x end fraction close parentheses plus 1 over denominator open parentheses fraction numerator 1 plus 8 x over denominator 2 x end fraction close parentheses minus 3 end fraction end cell row blank equals cell fraction numerator fraction numerator 1 plus 8 x plus 2 x over denominator 2 x end fraction over denominator fraction numerator 1 plus 8 x minus 6 x over denominator 2 x end fraction end fraction end cell row blank equals cell fraction numerator 10 x plus 1 over denominator 2 x plus 1 end fraction end cell end table end style

Jadi, begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses x close parentheses equals fraction numerator 10 x plus 1 over denominator 2 x plus 1 end fraction end style.

54

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Diketahui fungsi f(x)=3x−1 dan g(x)=2x2−3. Fungsi komposisi (gof)(x)=… +3mu.

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