Pertanyaan

Diketahui fungsi g ( x ) = 2 x + 5 dan ( f ∘ g ) ( x ) = 4 x 2 + 20 x + 23 . Rumus fungsi f ( x ) adalah ....

Diketahui fungsi $g (x) = 2 x + 5$ dan $(f \circ g) (x) = 4 x^{2} + 20 x + 23$ . Rumus fungsi $f (x)$ adalah ....

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Jawaban terverifikasi

Jawaban

jawaban yang tepat adalah A.

Pembahasan

Kita mempunyai Pertama kita mencari . Misal , maka Jadi, kita peroleh . Ingat rumus di bawah ini! dan . Dengan demikian, Jadi, jawaban yang tepat adalah A.

Kita mempunyai

Pertama kita mencari . Misal , maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g left parenthesis x right parenthesis end cell equals cell 2 x plus 5 end cell row y equals cell 2 x plus 5 end cell row cell 2 x end cell equals cell y minus 5 end cell row x equals cell fraction numerator y minus 5 over denominator 2 end fraction end cell end table end style$

Jadi, kita peroleh $begin mathsize 14px style g to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator x minus 5 over denominator 2 end fraction end style$ .

Ingat rumus di bawah ini!

dan .

Dengan demikian,

$begin mathsize 14px style 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 4 x squared plus 20 x plus 23 end cell row cell left parenthesis f ring operator g right parenthesis left parenthesis g to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis end cell equals cell 4 left parenthesis g to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis squared plus 20 left parenthesis g to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis plus 23 end cell row cell left parenthesis f ring operator g ring operator g to the power of negative 1 end exponent right parenthesis left parenthesis x right parenthesis end cell equals cell 4 left parenthesis g to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis squared plus 20 left parenthesis g to the power of negative 1 end exponent left parenthesis x right parenthesis right parenthesis plus 23 end cell row cell left parenthesis f ring operator I right parenthesis left parenthesis x right parenthesis end cell equals cell 4 left parenthesis fraction numerator x minus 5 over denominator 2 end fraction right parenthesis squared plus 20 left parenthesis fraction numerator x minus 5 over denominator 2 end fraction right parenthesis plus 23 end cell row cell f left parenthesis x right parenthesis end cell equals cell 4 left parenthesis left parenthesis x minus 5 right parenthesis squared over 2 squared right parenthesis plus 10 left parenthesis x minus 5 right parenthesis plus 23 end cell row cell f left parenthesis x right parenthesis end cell equals cell 4 left parenthesis fraction numerator x squared minus 10 x plus 25 over denominator 4 end fraction right parenthesis plus 10 x minus 50 plus 23 end cell row cell f left parenthesis x right parenthesis end cell equals cell x squared minus 10 x plus 25 plus 10 x minus 50 plus 23 end cell row cell f left parenthesis x right parenthesis end cell equals cell x squared plus left parenthesis negative 10 x plus 10 x right parenthesis plus 25 minus 50 plus 23 end cell row cell f left parenthesis x right parenthesis end cell equals cell x squared minus 2 end cell end table end style$

Jadi, jawaban yang tepat adalah A.