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Diketahui fungsi   dan .  Jika , maka tentukan nil...

Diketahui fungsi  begin mathsize 14px style f open parentheses x close parentheses equals a x plus b comma space f open parentheses 1 close parentheses equals 5 end style dan begin mathsize 14px style g open parentheses x close parentheses equals x squared plus 1 end style.  Jika begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses 2 close parentheses equals 10 end style, maka tentukan nilai begin mathsize 14px style a end styleyang memenuhi. (clue : ubah begin mathsize 14px style f open parentheses 1 close parentheses end style ke bentuk begin mathsize 14px style f open parentheses x close parentheses equals a x plus b end style)

Jawaban:

Diketahui fungsi  begin mathsize 14px style f open parentheses x close parentheses equals a x plus b comma space f open parentheses 1 close parentheses equals 5 end style dan begin mathsize 14px style g open parentheses x close parentheses equals x squared plus 1 end style.  Jika begin mathsize 14px style open parentheses g ring operator f close parentheses open parentheses 2 close parentheses equals 10 end style, maka tentukan nilai begin mathsize 14px style a end style yang memenuhi. adalah 

begin mathsize 14px style table attributes columnalign right center left columnspacing 2px end attributes row cell f open parentheses x close parentheses end cell equals cell a x plus b end cell row cell f left parenthesis 1 right parenthesis end cell equals cell a plus b end cell row 5 equals cell a plus b end cell row b equals cell 5 minus a end cell row blank blank blank 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 cell left parenthesis g ring operator f right parenthesis left parenthesis 2 right parenthesis end cell equals cell g open parentheses f open parentheses 2 close parentheses close parentheses end cell row 10 equals cell g open parentheses 2 a plus b close parentheses end cell row 10 equals cell open parentheses 2 a plus b close parentheses squared plus 1 end cell row 9 equals cell open parentheses 2 a plus 5 minus a close parentheses squared end cell row 9 equals cell open parentheses a plus 5 close parentheses squared end cell row cell left parenthesis a plus 5 right parenthesis squared end cell equals 9 row cell a squared plus 10 a plus 25 end cell equals 9 row cell a squared plus 10 a plus 16 end cell equals 0 row cell open parentheses a plus 8 close parentheses open parentheses a plus 2 close parentheses end cell equals 0 row cell a equals negative 8 end cell atau cell a equals negative 2 end cell end table end style  

Jadi, nilai a yang memenuhi adalah -8 atau -2

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