Pertanyaan

Diberikan f : R → R dengan f ( x ) = x − 2 5 x + 1 , x  = 2 .Jika f − 1 menyatakan invers dari f . Hitunglah f − 1 ( 2 1 ) + f − 1 ( 3 ) .

Diberikan $f : R \to R$ dengan $f (x) = \frac{5 x + 1}{x - 2}, x \neq = 2$ . Jika $f^{- 1}$ menyatakan invers dari $f$ . Hitunglah $f^{- 1} (\frac{1}{2}) + f^{- 1} (3)$ .

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

.

Pembahasan

Misalkan , maka Maka invers dari adalah . Sehingga Jadi .

$begin mathsize 14px style f open parentheses x close parentheses equals fraction numerator 5 x plus 1 over denominator x minus 2 end fraction comma space x not equal to 2 end style$

Misalkan , maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row straight y equals cell fraction numerator 5 straight x plus 1 over denominator straight x minus 2 end fraction end cell row cell straight y left parenthesis straight x minus 2 right parenthesis end cell equals cell 5 straight x plus 1 end cell row cell yx minus 2 straight y end cell equals cell 5 straight x plus 1 end cell row cell yx minus 5 straight x end cell equals cell 2 straight y plus 1 end cell row cell straight x left parenthesis straight y minus 5 right parenthesis end cell equals cell 2 straight y plus 1 end cell row straight x equals cell fraction numerator 2 straight y plus 1 over denominator straight y minus 5 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 2 x plus 1 over denominator x minus 5 end fraction end cell end table end style$

Maka invers dari adalah $begin mathsize 14px style f to the power of negative 1 end exponent open parentheses x close parentheses equals fraction numerator 2 x plus 1 over denominator x minus 5 end fraction end style$ .

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses 1 half close parentheses end cell equals cell fraction numerator 2 open parentheses begin display style 1 half end style close parentheses plus 1 over denominator open parentheses begin display style 1 half end style minus 5 close parentheses end fraction end cell row blank equals cell fraction numerator 1 plus 1 over denominator begin display style 1 half end style minus begin display style 10 over 2 end style end fraction end cell row blank equals cell fraction numerator 2 over denominator negative begin display style 9 over 2 end style end fraction end cell row blank equals cell negative 4 over 9 end cell row blank blank blank row cell f to the power of negative 1 end exponent open parentheses 3 close parentheses end cell equals cell fraction numerator 2 open parentheses 3 close parentheses plus 1 over denominator open parentheses 3 close parentheses minus 5 end fraction end cell row blank equals cell fraction numerator 6 plus 1 over denominator negative 2 end fraction end cell row blank equals cell negative 7 over 2 end cell end table end style$

Sehingga

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f to the power of negative 1 end exponent open parentheses 1 half close parentheses plus f to the power of negative 1 end exponent open parentheses 3 close parentheses end cell equals cell negative 4 over 9 plus open parentheses negative 7 over 2 close parentheses end cell row blank equals cell negative 4 over 9 minus 7 over 2 end cell row blank equals cell fraction numerator negative 8 minus 63 over denominator 18 end fraction end cell row blank equals cell negative 71 over 18 end cell end table end style$

Jadi .