Pertanyaan

Invers dari fungsi f ( x ) = 3 x − 4 7 x + 5 , x  = 3 4 adalah f − 1 ( x ) = ...

Invers dari fungsi $f (x) = \frac{7 x + 5}{3 x - 4}, x \neq = \frac{4}{3}$ adalah $f^{- 1} (x) = ...$

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E. Lestari

Master Teacher

Mahasiswa/Alumni Universitas Sebelas Maret

Jawaban terverifikasi

Jawaban

invers dari fungsi adalah .

invers dari fungsi $begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 7 x plus 5 over denominator 3 x minus 4 end fraction comma space x not equal to 4 over 3 space end style$ adalah $begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 4 x plus 5 over denominator 3 x minus 7 end fraction comma space x not equal to 7 over 3 end style$ .

Pembahasan

Menentukan invers Jadi, invers dari fungsi adalah .

Menentukan invers

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f left parenthesis x right parenthesis end cell equals cell fraction numerator 7 x plus 5 over denominator 3 x minus 4 end fraction end cell row y equals cell fraction numerator 7 x plus 5 over denominator 3 x minus 4 end fraction end cell row cell y left parenthesis 3 x minus 4 right parenthesis end cell equals cell 7 x plus 5 end cell row cell 3 x y minus 4 y end cell equals cell 7 x plus 5 end cell row cell 3 x y minus 7 x end cell equals cell 4 y plus 5 end cell row cell x left parenthesis 3 y minus 7 right parenthesis end cell equals cell 4 y plus 5 end cell row x equals cell fraction numerator 4 y plus 5 over denominator 3 y minus 7 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis y right parenthesis end cell equals cell fraction numerator 4 y plus 5 over denominator 3 y minus 7 end fraction end cell row cell f to the power of negative 1 end exponent left parenthesis x right parenthesis end cell equals cell fraction numerator 4 x plus 5 over denominator 3 x minus 7 end fraction semicolon space x not equal to 7 over 3 end cell row blank blank blank end table end style$

Jadi, invers dari fungsi $begin mathsize 14px style f left parenthesis x right parenthesis equals fraction numerator 7 x plus 5 over denominator 3 x minus 4 end fraction comma space x not equal to 4 over 3 space end style$ adalah $begin mathsize 14px style f to the power of negative 1 end exponent left parenthesis x right parenthesis equals fraction numerator 4 x plus 5 over denominator 3 x minus 7 end fraction comma space x not equal to 7 over 3 end style$ .