Pertanyaan

Jika f ( x ) = 3 x − 2 dan g ( x ) = x − 5 x + 2 , fungsi ( g ∘ f ) − 1 ( x ) = ....

Jika $f (x) = 3 x - 2$ dan $g (x) = \frac{x + 2}{x - 5},$ fungsi $(g \circ f)^{- 1} (x) = ....$

$begin mathsize 14px style fraction numerator 3 straight x over denominator 3 straight x minus 7 end fraction end style$

D. Entry

Master Teacher

Jawaban terverifikasi

Jawaban

Jawaban yang benar adalah E

Pembahasan

Diketahui: dan Ditanya: fungsi Jawab, Dengan menerapkan konsep fungsi komposisi, Dengan menerapkan konsepinvers fungsi, Misalkan maka: Jadi,Jika dan fungsi . Oleh karena itu, Jawaban yang benar adalah E

Diketahui:

dan

Ditanya:

fungsi

Jawab,

Dengan menerapkan konsep fungsi komposisi,

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis straight g ring operator straight f right parenthesis left parenthesis straight x right parenthesis end cell equals cell straight g left parenthesis straight f left parenthesis straight x right parenthesis right parenthesis end cell row blank equals cell straight g left parenthesis 3 straight x minus 2 right parenthesis end cell row blank equals cell fraction numerator left parenthesis 3 straight x minus 2 right parenthesis plus 2 over denominator left parenthesis 3 straight x minus 2 right parenthesis minus 5 end fraction end cell row blank equals cell fraction numerator 3 straight x over denominator 3 straight x minus 7 end fraction end cell end table end style$

Dengan menerapkan konsep invers fungsi,

Misalkan maka:

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight y equals cell left parenthesis straight g ring operator straight f right parenthesis left parenthesis straight x right parenthesis end cell row straight y equals cell fraction numerator 3 straight x over denominator 3 straight x minus 7 end fraction end cell row cell straight y left parenthesis 3 straight x minus 7 right parenthesis end cell equals cell 3 straight x end cell row cell 3 xy minus 7 straight y end cell equals cell 3 straight x end cell row cell 3 xy minus 3 straight x end cell equals cell 7 straight y end cell row cell straight x left parenthesis 3 straight y minus 3 right parenthesis end cell equals cell 7 straight y end cell row straight x equals cell fraction numerator 7 straight y over denominator 3 straight y minus 3 end fraction end cell row cell left parenthesis straight g ring operator straight f right parenthesis to the power of negative 1 end exponent left parenthesis straight y right parenthesis end cell equals cell fraction numerator 7 straight y over denominator 3 straight y minus 3 end fraction end cell row cell left parenthesis straight g ring operator straight f right parenthesis blank to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell equals cell fraction numerator 7 straight x over denominator 3 straight x minus 3 end fraction end cell end table end style$

Jadi, Jika dan fungsi $begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell left parenthesis straight g ring operator straight f right parenthesis to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 7 straight x over denominator 3 straight x minus 3 end fraction end cell end table end style$ .

Oleh karena itu, Jawaban yang benar adalah E