Jika f∘g(x)=4x+7, g(x)=2x−1, tentukan rumus fungsi f(x)

Pertanyaan

Jika begin mathsize 14px style f ring operator g left parenthesis x right parenthesis equals 4 x plus 7 end styleundefined, tentukan rumus fungsi begin mathsize 14px style f left parenthesis x right parenthesis end style 

E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

rumus fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x plus 9 end style.

Pembahasan

Diketahui begin mathsize 14px style f ring operator g left parenthesis x right parenthesis equals 4 x plus 7 space end style dan  begin mathsize 14px style g open parentheses x close parentheses equals 2 x minus 1 end style.

Perhatikan bahwa

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f ring operator g left parenthesis x right parenthesis end cell equals cell 4 x plus 7 space end cell row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell 4 x plus 7 space end cell row cell f left parenthesis 2 x minus 1 right parenthesis end cell equals cell 4 x plus 7 end cell end table end style 

Misalkan begin mathsize 14px style 2 x minus 1 equals a end style.

Maka 

 begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell 2 x end cell equals cell a plus 1 end cell row x equals cell fraction numerator a plus 1 over denominator 2 end fraction end cell end table end style 

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis 2 x minus 1 right parenthesis end cell equals cell 4 x plus 7 space end cell row cell f left parenthesis a right parenthesis end cell equals cell 4. fraction numerator a plus 1 over denominator 2 end fraction plus 7 space end cell row cell f left parenthesis a right parenthesis end cell equals cell 2 left parenthesis a plus 1 right parenthesis plus 7 end cell row cell f left parenthesis a right parenthesis end cell equals cell 2 a plus 2 plus 7 space end cell row cell f left parenthesis a right parenthesis end cell equals cell 2 a plus 9 space end cell row cell f left parenthesis x right parenthesis end cell equals cell 2 x plus 9 end cell end table end style 

Jadi, rumus fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x plus 9 end style.

22

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Pertanyaan serupa

Diketahui g(x)=2x+4 dan f∘g(x)=4x2+16x−3 Tentukan Nilai dari f−1(−1).

31

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Jawaban terverifikasi

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