Fungsi f: R→R didefinisikan oleh f(x) =3−x4x−7​, x=3. Invers dari f(x) adalah f−1(x) =....

Pertanyaan

Fungsi f colon space R rightwards arrow R didefinisikan oleh straight f left parenthesis straight x right parenthesis space equals fraction numerator 4 straight x minus 7 over denominator 3 minus straight x end fraction comma space straight x not equal to 3. Invers dari f left parenthesis x right parenthesis adalah straight f to the power of negative 1 end exponent left parenthesis straight x right parenthesis space equals.... 

  1. fraction numerator 3 x minus 7 over denominator x minus 4 end fraction comma x not equal to 4 

  2. fraction numerator 3 x minus 7 over denominator x plus 4 end fraction comma x not equal to negative 4 

  3. fraction numerator 3 x minus 3 over denominator x minus 4 end fraction comma x not equal to 4 

  4. fraction numerator 3 x plus 7 over denominator x plus 4 end fraction comma x not equal to negative 4 

  5. fraction numerator 3 x plus 7 over denominator x minus 4 end fraction comma x not equal to 4 

R. RGFLLIMA

Master Teacher

Jawaban terverifikasi

Jawaban

Jawaban yang benar adalah D

Pembahasan

Invers fungsi rasional.

Misalkan straight y equals straight f left parenthesis straight x right parenthesis space maka space straight x equals straight f to the power of negative 1 end exponent left parenthesis straight x right parenthesis sehingga diperoleh :

table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x right parenthesis space end cell equals cell fraction numerator 4 straight x minus 7 over denominator 3 minus straight x end fraction end cell row cell straight y space end cell equals cell fraction numerator 4 straight x minus 7 over denominator 3 minus straight x end fraction end cell row cell straight y left parenthesis 3 minus straight x right parenthesis end cell equals cell 4 straight x minus 7 end cell row cell 3 straight y minus xy end cell equals cell 4 straight x minus 7 end cell row cell negative 4 straight x minus xy end cell equals cell negative 3 straight y minus 7 end cell row cell straight x left parenthesis negative 4 minus straight y right parenthesis end cell equals cell negative 3 straight y minus 7 end cell row straight x equals cell fraction numerator negative 3 straight y minus 7 over denominator negative 4 minus straight y end fraction end cell row blank equals cell fraction numerator 3 straight y plus 7 over denominator 4 plus straight y end fraction end cell row cell straight f to the power of negative 1 end exponent left parenthesis straight y right parenthesis end cell equals cell fraction numerator 3 straight y plus 7 over denominator 4 plus straight y end fraction end cell row cell straight f to the power of negative 1 end exponent left parenthesis straight x right parenthesis end cell equals cell fraction numerator 3 straight x plus 7 over denominator straight x plus 4 end fraction end cell end table 

Jadiii, table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight f 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 3 straight x plus 7 over denominator straight x plus 4 end fraction end cell end table 

Oleh karena itu, Jawaban yang benar adalah D

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