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Diketahui fungsi f(x)=2x+1 dan (f∘g)(x+1)=−2x2−4x−1. NIlai g(−2) adalah...

Pertanyaan

Diketahui fungsi begin mathsize 14px style f open parentheses x close parentheses equals 2 x plus 1 end style dan begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x plus 1 close parentheses equals negative 2 x squared minus 4 x minus 1 end style. NIlai begin mathsize 14px style g open parentheses negative 2 close parentheses end style adalah...

  1. begin mathsize 14px style negative 5 end stylespace space

  2. begin mathsize 14px style negative 4 end stylespace space

  3. begin mathsize 14px style negative 1 end stylespace space

  4. begin mathsize 14px style 1 end stylespace space

  5. begin mathsize 14px style 5 end stylespace space

T. Rizki

Master Teacher

Jawaban terverifikasi

Jawaban

jawaban yang benar adalah B.

Pembahasan

Diketahui:

table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 2 x plus 1 end cell row cell open parentheses f ring operator g close parentheses open parentheses x plus 1 close parentheses end cell equals cell negative 2 x squared minus 4 x minus 1 end cell end table

Ditanya: g open parentheses negative 2 close parentheses ?

Tentukan fungsi begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses end style terlebih dahulu

Misalkan

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell x plus 1 end cell equals a row x equals cell a minus 1 end cell end table end style

Sehingga

begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x plus 1 close parentheses end cell equals cell negative 2 x squared minus 4 x minus 1 end cell row cell open parentheses f ring operator g close parentheses open parentheses a close parentheses end cell equals cell negative 2 open parentheses a minus 1 close parentheses squared minus 4 open parentheses a minus 1 close parentheses minus 1 end cell row cell open parentheses f ring operator g close parentheses open parentheses a close parentheses end cell equals cell negative 2 open parentheses a squared minus 2 a plus 1 close parentheses minus 4 open parentheses a minus 1 close parentheses minus 1 end cell row cell open parentheses f ring operator g close parentheses open parentheses a close parentheses end cell equals cell negative 2 a squared plus 4 a minus 2 minus 4 a plus 4 minus 1 end cell row cell open parentheses f ring operator g close parentheses open parentheses a close parentheses end cell equals cell negative 2 a squared plus 1 end cell row blank blank blank end table end style

Jadi

 table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell negative 2 x squared plus 1 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell negative 2 x squared plus 1 end cell row cell 2 g open parentheses x close parentheses plus 1 end cell equals cell negative 2 x squared plus 1 end cell row cell 2 g open parentheses x close parentheses end cell equals cell negative 2 x squared end cell row cell g open parentheses x close parentheses end cell equals cell negative x squared end cell end table

Substitusikan x equals negative 2 ke dalam fungsi g left parenthesis x right parenthesis maka didapatkan

table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses negative 2 close parentheses end cell equals cell negative open parentheses negative 2 close parentheses squared end cell row blank equals cell negative 4 end cell end table 

Dengan demikian, nilai begin mathsize 14px style g open parentheses negative 2 close parentheses equals negative 4 end style.

Oleh karena itu, jawaban yang benar adalah B.

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