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Diketahui fungsi f(x)=2x+3 dan g(x)=x2−2x+4. Carilah fungsi (g∘f)(x)=....

Pertanyaan

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x plus 3 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x squared minus 2 x plus 4 end style. Carilah fungsi begin mathsize 14px style left parenthesis g ring operator f right parenthesis left parenthesis x right parenthesis equals.... end style 

  1. ...space 

  2. ...space 

K. Prameswari

Master Teacher

Mahasiswa/Alumni Universitas Gadjah Mada

Jawaban terverifikasi

Jawaban

diperoleh fungsi begin mathsize 14px style begin bold style left parenthesis g ring operator f right parenthesis end style begin bold style left parenthesis x right parenthesis end style bold equals bold 4 bold italic x to the power of bold 2 bold plus bold 8 bold italic x bold plus bold 7 end style

Pembahasan

Diketahui fungsi begin mathsize 14px style f left parenthesis x right parenthesis equals 2 x plus 3 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals x squared minus 2 x plus 4 end style. Maka dapat diperoleh

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 2 x plus 3 close parentheses end cell row blank equals cell open parentheses 2 x plus 3 close parentheses squared minus 2 open parentheses 2 x plus 3 close parentheses plus 4 end cell row blank equals cell 4 x squared plus 12 x plus 9 minus 4 x minus 6 plus 4 end cell row blank equals cell 4 x squared plus 8 x plus 7 end cell end table end style

Jadi, diperoleh fungsi begin mathsize 14px style begin bold style left parenthesis g ring operator f right parenthesis end style begin bold style left parenthesis x right parenthesis end style bold equals bold 4 bold italic x to the power of bold 2 bold plus bold 8 bold italic x bold plus bold 7 end style

48

2.6 (3 rating)

Pertanyaan serupa

3. Perhatikan  Jika diketahui fungsi f(x)=2x−1 dan fungsi  g(x)=x−32x+1​.  Tentukan : c. (f∘g)(−4)

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Jawaban terverifikasi

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