Pertanyaan

Jika f ( x ) = 3 x + 5 dan g ( x ) = 2 x + 3 x − 2 , x  = − 2 3 , hitunglah ( f ∘ g ) − 1 ( 6 ) + ( g ∘ f ) − 1 ( − 1 ) .

Jika $f (x) = 3 x + 5 dan g (x) = \frac{x - 2}{2 x + 3}, x \neq = - \frac{3}{2}$ , hitunglah $(f \circ g)^{- 1} (6) + (g \circ f)^{- 1} (- 1)$ .

Ikuti Tryout SNBT & Menangkan E-Wallet 100rb

Habis dalam

Klaim

L. Rante

Master Teacher

Mahasiswa/Alumni Universitas Negeri Makassar

Jawaban terverifikasi

Jawaban

.

begin mathsize 14px style left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis 6 right parenthesis plus left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis equals negative 52 over 63 end style

Pembahasan

Menentukan invers fungsi Menentukan invers fungsi Menentukan menentukan Maka Jadi .

Menentukan invers fungsi

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell f open parentheses x close parentheses end cell equals cell 3 x plus 5 end cell row y equals cell 3 x plus 5 end cell row cell 3 x end cell equals cell y minus 5 end cell row x equals cell fraction numerator y minus 5 over denominator 3 end fraction end cell row cell f to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator x minus 5 over denominator 3 end fraction end cell end table end style$

Menentukan invers fungsi

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell g open parentheses x close parentheses end cell equals cell fraction numerator x minus 2 over denominator 2 x plus 3 end fraction end cell row y equals cell fraction numerator x minus 2 over denominator 2 x plus 3 end fraction end cell row cell y open parentheses 2 x plus 3 close parentheses end cell equals cell x minus 2 end cell row cell 2 x y plus 3 y end cell equals cell x minus 2 end cell row cell 2 x y minus x end cell equals cell negative 3 y minus 2 end cell row cell x open parentheses 2 y minus 1 close parentheses end cell equals cell negative 3 y minus 2 end cell row x equals cell fraction numerator negative 3 y minus 2 over denominator 2 y minus 1 end fraction end cell row cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator negative 3 x minus 2 over denominator 2 x minus 1 end fraction end cell end table end style$

Menentukan

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

menentukan

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell open parentheses g ring operator f close parentheses to the power of negative 1 end exponent open parentheses negative 1 close parentheses end cell equals cell open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses negative 1 close parentheses end cell row blank blank blank row cell g to the power of negative 1 end exponent open parentheses negative 1 close parentheses end cell equals cell fraction numerator negative 3 open parentheses negative 1 close parentheses minus 2 over denominator 2 open parentheses negative 1 close parentheses minus 1 end fraction end cell row blank equals cell negative 1 third end cell row blank blank blank row cell open parentheses f to the power of negative 1 end exponent ring operator g to the power of negative 1 end exponent close parentheses open parentheses negative 1 close parentheses end cell equals cell f to the power of negative 1 end exponent open parentheses g to the power of negative 1 end exponent open parentheses negative 1 close parentheses close parentheses end cell row blank equals cell f to the power of negative 1 end exponent open parentheses negative 1 third close parentheses end cell row blank equals cell fraction numerator negative begin display style 1 third end style minus 5 over denominator 3 end fraction end cell row blank equals cell fraction numerator negative begin display style 16 over 3 end style over denominator 3 end fraction end cell row blank equals cell negative 16 over 9 end cell end table end style$

Maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis 6 right parenthesis plus left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis end cell equals cell fraction numerator 9 over denominator 7 end fraction plus open parentheses negative 19 over 9 close parentheses end cell row blank equals cell 9 over 7 minus 19 over 9 end cell row blank equals cell fraction numerator 81 minus 133 over denominator 63 end fraction end cell row blank equals cell negative 52 over 63 end cell end table end style$

Jadi begin mathsize 14px style left parenthesis f ring operator g right parenthesis to the power of negative 1 end exponent left parenthesis 6 right parenthesis plus left parenthesis g ring operator f right parenthesis to the power of negative 1 end exponent left parenthesis negative 1 right parenthesis equals negative 52 over 63 end style .