Diketahui g(x)=x−1 dan (f∘g)(x)=4x2−x, tentukan nilai f(x) !

Pertanyaan

Diketahui size 14px g begin mathsize 14px style left parenthesis x right parenthesis end style size 14px equals size 14px x size 14px minus size 14px 1 dan begin mathsize 14px style open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 4 x squared minus x end style, tentukan nilai size 14px f begin mathsize 14px style left parenthesis x right parenthesis end style !

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Y. Endah

Master Teacher

Mahasiswa/Alumni Institut Teknologi Bandung

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begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell equals cell x minus 1 end cell row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell 4 x squared minus x end cell row cell misal colon space f open parentheses x close parentheses end cell equals cell a x squared plus b x plus c end cell row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell 4 x squared minus x end cell row cell f open parentheses x minus 1 close parentheses end cell equals cell 4 x squared minus x end cell row cell a open parentheses x minus 1 close parentheses squared plus b open parentheses x minus 1 close parentheses plus c end cell equals cell 4 x squared minus x end cell row cell a open parentheses x squared minus 2 x plus 1 close parentheses plus b x minus b plus c end cell equals cell 4 x squared minus x end cell row cell a x squared minus 2 a x plus a plus b x minus b plus c end cell equals cell 4 x squared minus x end cell row a equals 4 row cell negative 2 a plus b end cell equals 1 row cell negative 8 plus b end cell equals 1 row b equals 9 row cell a minus b plus c end cell equals 0 row cell 4 minus 9 plus c end cell equals 0 row c equals 5 end table end style 

sehingga diperoleh begin mathsize 14px style f open parentheses x close parentheses equals 4 x squared plus 9 x plus 5 end style.

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Diketahui fungsi  f(x)=ax+b, f(1)=5 dan g(x)=x2+1.  Jika (g∘f)(2)=10, maka tentukan nilai ayang memenuhi. (clue : ubah f(1) ke bentuk f(x)=ax+b)

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