Pertanyaan

Jika diketahui g ( x ) = 2 x + 6 dan ( f ∘ g ) ( x ) = 4 x 2 + 22 x + 18 , maka fungsi f ( x ) adalah ...

Jika diketahui $g (x) = 2 x + 6$ dan $(f \circ g) (x) = 4 x^{2} + 22 x + 18$ , maka fungsi $f (x)$ adalah ...

S. Ayu

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Prof. DR. Hamka

Jawaban terverifikasi

Pembahasan

Misal: , maka: Kemudian substitusi ke fungsi komposisi . Maka, fungsi adalah .

Misal:

a equals 2 x plus 6 , maka:

$table attributes columnalign right center left columnspacing 0px end attributes row a equals cell 2 x plus 6 end cell row cell 2 x end cell equals cell a minus 6 end cell row x equals cell fraction numerator a minus 6 over denominator 2 end fraction end cell end table$

Kemudian substitusi ke fungsi komposisi open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 4 x squared plus 22 x plus 18 .

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses open parentheses x close parentheses end cell equals cell 4 x squared plus 22 x plus 18 end cell row cell f open parentheses g open parentheses x close parentheses close parentheses end cell equals cell equals 4 x squared plus 22 x plus 18 end cell row cell f open parentheses 2 x plus 6 close parentheses end cell equals cell 4 x squared plus 22 x plus 18 end cell row cell f open parentheses a close parentheses end cell equals cell 4 open parentheses fraction numerator a minus 6 over denominator 2 end fraction close parentheses squared plus 22 open parentheses fraction numerator a minus 6 over denominator 2 end fraction close parentheses plus 18 end cell row cell f open parentheses a close parentheses end cell equals cell 4 open parentheses fraction numerator a squared minus 12 a plus 36 over denominator 4 end fraction close parentheses plus 11 a minus 66 plus 18 end cell row cell f open parentheses a close parentheses end cell equals cell a squared minus 12 a plus 36 plus 11 a minus 48 end cell row cell f open parentheses a close parentheses end cell equals cell a squared minus a minus 12 end cell row cell f open parentheses x close parentheses end cell equals cell x squared minus x minus 12 end cell end table$

Maka, fungsi f open parentheses x close parentheses adalah Error converting from MathML to accessible text. .