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Diketahui fungsi . Jika diketahui  dan , fungsi  adalah ...

Pertanyaan

Diketahui fungsi f colon space straight real numbers rightwards arrow straight real numbers space dan space g space colon space straight real numbers rightwards arrow straight real numbers. Jika diketahui f left parenthesis 2 x plus 1 right parenthesis equals 6 x – 9 dan g left parenthesis x minus 2 right parenthesis equals x squared plus 4 x, fungsi left parenthesis f space ring operator space g right parenthesis left parenthesis x right parenthesis adalah ...

  1. 3 x squared plus 12 x plus 24 

  2. 3 x squared plus 12 x plus 48 

  3. 3 x squared plus 24 x plus 12 

  4. 3 x squared plus 24 x plus 24 

  5. 3 x squared plus 24 x plus 36 

Pembahasan Soal:

Diketahui: 

f left parenthesis 2 x plus 1 right parenthesis equals 6 x – 9
g left parenthesis x minus 2 right parenthesis equals x squared plus 4 x

Mencari f left parenthesis x right parenthesis space dan space g left parenthesis x right parenthesis:

table attributes columnalign right center left columnspacing 0px end attributes row y equals cell 2 x plus 1 end cell row cell 2 x end cell equals cell y minus 1 end cell row x equals cell 1 half y minus 1 half end cell row blank rightwards double arrow cell y equals 1 half x minus 1 half end cell row cell f open parentheses x close parentheses end cell equals cell 6 x minus 9 end cell row cell f left parenthesis x right parenthesis end cell equals cell 6 open parentheses 1 half x minus 1 half close parentheses minus 9 end cell row cell f open parentheses x close parentheses end cell equals cell 3 x minus 3 minus 9 end cell row cell f left parenthesis x right parenthesis end cell equals cell 3 x minus 12 end cell row blank blank blank row y equals cell x minus 2 end cell row x equals cell y plus 2 end cell row blank rightwards double arrow cell y equals x plus 2 end cell row cell g open parentheses x close parentheses end cell equals cell x squared plus 4 x blank end cell row cell g open parentheses x close parentheses end cell equals cell open parentheses x plus 2 close parentheses squared plus 4 open parentheses x plus 2 close parentheses end cell row cell g open parentheses x close parentheses end cell equals cell x squared plus 4 x plus 4 plus 4 x plus 8 end cell row cell g open parentheses x close parentheses end cell equals cell x squared plus 8 x plus 12 end cell end table  

Mencari left parenthesis f space ring operator space g right parenthesis left parenthesis x right parenthesis:

table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell f open parentheses x squared plus 8 x plus 12 close parentheses end cell row blank equals cell f open parentheses x squared plus 8 x plus 12 close parentheses end cell row blank equals cell 3 open parentheses x squared plus 8 x plus 12 close parentheses minus 12 end cell row blank equals cell 3 x squared plus 24 x plus 36 minus 12 end cell row blank equals cell 3 x squared plus 24 x plus 12 end cell end table   

Jadi, hasil dari left parenthesis f space ring operator space g right parenthesis left parenthesis x right parenthesis adalah 3 x squared plus 24 x plus 24.

Dengan demikian, jawaban yang tepat adalah D.

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 06 Mei 2021

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