Pertanyaan

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

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

S. Surya

Master Teacher

Jawaban terverifikasi

Jawaban

i, Invers adalah

i, Invers $straight f left parenthesis straight x right parenthesis equals fraction numerator 4 straight x minus 7 over denominator 3 minus straight x end fraction comma straight x not equal to 3$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight f apostrophe left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 straight x plus 7 over denominator 4 plus x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table$

Pembahasan

Dengan menerapkan konsep invers fungsi: maka: Jadii, Invers adalah

Dengan menerapkan konsep invers fungsi:

straight y equals straight f left parenthesis straight x right parenthesis rightwards arrow straight x equals straight f apostrophe left parenthesis straight y right parenthesis

maka:

$table attributes columnalign right center left columnspacing 0px end attributes row cell straight f left parenthesis straight x right parenthesis end cell equals cell fraction numerator 4 straight x minus 7 over denominator 3 minus straight x end fraction end cell row y equals cell fraction numerator 4 straight x minus 7 over denominator 3 minus straight x end fraction end cell row cell y left parenthesis 3 minus straight x right parenthesis end cell equals cell 4 straight x minus 7 end cell row cell 3 straight y minus xy end cell equals cell 4 straight x minus 7 end cell row cell negative 4 straight x minus xy end cell equals cell negative 3 straight y minus 7 end cell row cell straight x left parenthesis negative 4 minus straight y right parenthesis end cell equals cell negative 3 straight y minus 7 end cell row straight x equals cell fraction numerator negative 3 straight y minus 7 over denominator negative 4 minus straight y end fraction end cell row blank equals cell fraction numerator negative left parenthesis 3 straight y plus 7 right parenthesis over denominator negative left parenthesis straight y plus 4 right parenthesis end fraction end cell row blank equals cell fraction numerator left parenthesis 3 straight y plus 7 right parenthesis over denominator left parenthesis straight y plus 4 right parenthesis end fraction end cell row cell straight f apostrophe left parenthesis straight y right parenthesis end cell equals cell fraction numerator left parenthesis 3 straight y plus 7 right parenthesis over denominator left parenthesis straight y plus 4 right parenthesis end fraction end cell row cell straight f apostrophe left parenthesis straight x right parenthesis end cell equals cell fraction numerator 3 straight x plus 7 over denominator straight x plus 4 end fraction end cell end table$

Jadii, Invers $straight f left parenthesis straight x right parenthesis equals fraction numerator 4 straight x minus 7 over denominator 3 minus straight x end fraction comma straight x not equal to 3$ adalah $table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell straight f apostrophe left parenthesis straight x right parenthesis end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 3 straight x plus 7 over denominator 4 plus x end fraction end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank. end table$