Roboguru

Diketahui  dan  dan jika , maka nilai  yang memenuhi adalah

Pertanyaan

Diketahui begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x squared minus 4 x plus 6 end style dan begin mathsize 14px style g left parenthesis x right parenthesis equals 2 x minus 1 end style dan jika begin mathsize 14px style f ring operator g left parenthesis x right parenthesis equals 101 end style, maka nilai begin mathsize 14px style x end style yang memenuhi adalah begin mathsize 14px style... end style 

Pembahasan Soal:

Diketahui :

begin mathsize 14px style f left parenthesis x right parenthesis equals 3 x squared minus 4 x plus 6 end style
begin mathsize 14px style g left parenthesis x right parenthesis equals 2 x minus 1 end style
begin mathsize 14px style f ring operator g left parenthesis x right parenthesis equals 101 end style

Ditanya :

nilai begin mathsize 14px style x end style yang memenuhi adalah

Jawab :

begin mathsize 14px style f ring operator g left parenthesis x right parenthesis equals f open parentheses g open parentheses x close parentheses close parentheses f ring operator g left parenthesis x right parenthesis equals f open parentheses 2 x minus 1 close parentheses f ring operator g left parenthesis x right parenthesis equals 3 open parentheses 2 x minus 1 close parentheses squared minus 4 open parentheses 2 x minus 1 close parentheses plus 6 f ring operator g left parenthesis x right parenthesis equals 3 open parentheses 4 x squared minus 4 x plus 1 close parentheses minus 8 x plus 4 plus 6 f ring operator g left parenthesis x right parenthesis equals 12 x squared minus 12 x plus 3 minus 8 x plus 4 plus 6 f ring operator g left parenthesis x right parenthesis equals 12 x squared minus 20 x plus 13 end style 

Karena begin mathsize 14px style f ring operator g left parenthesis x right parenthesis equals 101 end style, maka : 

begin mathsize 14px style f ring operator g left parenthesis x right parenthesis equals 12 x squared minus 20 x plus 13 101 equals 12 x squared minus 20 x plus 13 12 x squared minus 20 x plus 13 minus 101 equals 0 12 x squared minus 20 x minus 88 equals 0 space space space space left parenthesis masing space masing space di space bagi space 4 right parenthesis 3 straight x squared minus 5 straight x minus 22 equals 0 open parentheses straight x plus 2 close parentheses open parentheses 3 straight x minus 11 close parentheses equals 0 straight x plus 2 equals 0 space atau space 3 straight x minus 11 equals 0 space straight x equals negative 2 space space space space space space space space space space space space 3 straight x equals 11 space space space space space space space space space space space space space space space space space space space space space space space space space straight x equals 11 over 3 end style 

Jadi, nilai begin mathsize 14px style x end style yang memenuhi adalah begin mathsize 14px style x equals 2 end style atau begin mathsize 14px style x equals 11 over 3 end style 

Pembahasan terverifikasi oleh Roboguru

Terakhir diupdate 04 April 2021

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