Pertanyaan

Jika ( f ∘ g ) ( x ) = 10 x 2 − 8 x − 3 dan g ( x ) = 2 x + 4 maka f − 1 ( x ) = ...

Jika $(f \circ g) (x) = 10 x^{2} - 8 x - 3$ dan $g (x) = 2 x + 4$ maka $f^{- 1} (x) = ...$

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Jawaban terverifikasi

Jawaban

jawabannya tidak ada pada opsi, jawaban yang benar adalah

jawabannya tidak ada pada opsi, jawaban yang benar adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator left parenthesis 24 plus-or-minus square root of 10 x plus 46 end root right parenthesis over denominator 5 end fraction end cell end table$

Pembahasan

Diketahui dan maka : Sehingga: Jadi jawabannya tidak ada pada opsi, jawaban yang benar adalah

Diketahui open parentheses f ring operator g close parentheses open parentheses x close parentheses equals 10 x squared minus 8 x minus 3 dan g open parentheses x close parentheses equals 2 x plus 4 maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses f ring operator g close parentheses left parenthesis x right parenthesis end cell equals cell f left parenthesis g left parenthesis x right parenthesis right parenthesis end cell row cell 10 x squared minus 8 x minus 3 end cell equals cell f left parenthesis 2 x plus 4 right parenthesis end cell row cell misal space 2 x plus 4 end cell equals cell y comma space maka space x equals fraction numerator y minus 4 over denominator 2 end fraction end cell row cell 10 open parentheses fraction numerator y minus 4 over denominator 2 end fraction close parentheses squared minus 8 open parentheses fraction numerator y minus 4 over denominator 2 end fraction close parentheses minus 3 end cell equals cell f open parentheses 2 open parentheses fraction numerator y minus 4 over denominator 2 end fraction close parentheses plus 4 close parentheses end cell row cell 10 open parentheses fraction numerator y squared minus 8 y plus 16 over denominator 4 end fraction close parentheses minus 4 y plus 16 minus 3 end cell equals cell f left parenthesis y right parenthesis end cell row cell fraction numerator 10 y squared over denominator 4 end fraction minus fraction numerator 80 y over denominator 4 end fraction plus 160 over 4 minus 4 y plus 13 end cell equals cell f left parenthesis y right parenthesis end cell row cell 5 over 2 y squared minus 20 y plus 40 minus 4 y plus 13 end cell equals cell f left parenthesis y right parenthesis end cell row cell 5 over 2 y squared minus 24 y plus 53 end cell equals cell f left parenthesis y right parenthesis end cell row cell f left parenthesis x right parenthesis end cell equals cell 5 over 2 x squared minus 24 x plus 53 end cell end table$

Sehingga:

table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell 5 over 2 x squared minus 24 x plus 53 end cell row y equals cell 5 over 2 x squared minus 24 x plus 53 end cell row cell 2 y end cell equals cell 5 x squared minus 48 x plus 106 end cell end table

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$table attributes columnalign right center left columnspacing 0px end attributes row x equals cell fraction numerator negative b plus-or-minus square root of b squared minus 4 a c end root over denominator 2 a end fraction end cell row blank equals cell fraction numerator negative left parenthesis negative 48 right parenthesis plus-or-minus square root of left parenthesis negative 48 right parenthesis squared minus 4 left parenthesis 5 right parenthesis left parenthesis 106 minus 2 y right parenthesis end root over denominator 2 left parenthesis 5 right parenthesis end fraction end cell row blank equals cell fraction numerator 48 plus-or-minus square root of 2.304 minus 2.120 plus 40 y end root over denominator 10 end fraction end cell row blank equals cell fraction numerator 48 plus-or-minus square root of 40 y plus 184 end root over denominator 10 end fraction end cell row blank equals cell fraction numerator 2 left parenthesis 24 plus-or-minus square root of 10 y plus 46 end root right parenthesis over denominator 10 end fraction end cell row blank equals cell fraction numerator left parenthesis 24 plus-or-minus square root of 10 y plus 46 end root right parenthesis over denominator 5 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator left parenthesis 24 plus-or-minus square root of 10 x plus 46 end root right parenthesis over denominator 5 end fraction end cell end table$

Jadi jawabannya tidak ada pada opsi, jawaban yang benar adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator left parenthesis 24 plus-or-minus square root of 10 x plus 46 end root right parenthesis over denominator 5 end fraction end cell end table$