Pertanyaan

Diketahui jika fungsi f ( x ) = x + 3 dan ( f ∘ g ) − 1 ( x ) = 2 x − 7 , maka fungsi g ( x ) adalah...

Diketahui jika fungsi $f (x) = x + 3$ dan $(f \circ g)^{- 1} (x) = 2 x - 7$ , maka fungsi $g (x)$ adalah...

$fraction numerator x plus 2 over denominator 2 end fraction$
$fraction numerator x plus 3 over denominator 2 end fraction$
$fraction numerator x plus 7 over denominator 2 end fraction$
$fraction numerator x plus 1 over denominator 2 end fraction$
$fraction numerator x plus 4 over denominator 2 end fraction$

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Jawaban terverifikasi

Jawaban

jawaban yang benar adalah D.

Pembahasan

Menentukan Menentukan Jadi, jawaban yang benar adalah D.

Menentukan left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell 2 x minus 7 end cell row y equals cell 2 x minus 7 end cell row cell y plus 7 end cell equals cell 2 x end cell row cell fraction numerator y plus 7 over denominator 2 end fraction end cell equals x row cell fraction numerator y plus 7 over denominator 2 end fraction end cell equals cell left parenthesis f ring operator g right parenthesis left parenthesis y right parenthesis end cell row cell fraction numerator x plus 7 over denominator 2 end fraction end cell equals cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell end table$

Menentukan g left parenthesis x right parenthesis

$table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 7 over denominator 2 end fraction end cell row cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell equals cell fraction numerator x plus 7 over denominator 2 end fraction end cell row cell g left parenthesis x right parenthesis plus 3 end cell equals cell fraction numerator x plus 7 over denominator 2 end fraction end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 7 over denominator 2 end fraction minus 3 end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 7 over denominator 2 end fraction minus 6 over 2 end cell row cell g left parenthesis x right parenthesis end cell equals cell fraction numerator x plus 1 over denominator 2 end fraction end cell end table$

Jadi, jawaban yang benar adalah D.