Pertanyaan

Diketahui fungsi f ( x ) = 2 x + 5 , dan g ( x ) = x − 6 3 x + 2 , x  = 6. Jika invers fungsi f ( x ) = f − 1 ( x ) dan invers fungsi g ( x ) = g − 1 ( x ) . Tentukan: b. g − 1 ( x )

Diketahui fungsi $f (x) = 2 x + 5,$ dan $g (x) = \frac{3 x + 2}{x - 6}, x \neq = 6.$ Jika invers fungsi $f (x) = f^{- 1} (x)$ dan invers fungsi $g (x) = g^{- 1} (x)$ . Tentukan:

b. $g^{- 1} (x)$

F. Nur

Master Teacher

Mahasiswa/Alumni Universitas Muhammadiyah Malang

Jawaban terverifikasi

Jawaban

invers dari fungsi adalah

invers dari fungsi $begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator 3 x plus 2 over denominator x minus 6 end fraction comma space x not equal to 6 space end style$ adalah $begin mathsize 14px style g to the power of negative 1 end exponent table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 6 x plus 2 over denominator x minus 3 end fraction end cell end table comma space x not equal to 3. end style$

Pembahasan

Misalkan , maka Jadi, invers dari fungsi adalah

Misalkan begin mathsize 14px style g open parentheses x close parentheses equals y end style , maka

$begin mathsize 14px style table attributes columnalign right center left columnspacing 0px end attributes row cell fraction numerator 3 x plus 2 over denominator x minus 6 end fraction end cell equals y row cell 3 x plus 2 end cell equals cell y open parentheses x minus 6 close parentheses end cell row cell 3 x plus 2 end cell equals cell x y minus 6 y end cell row cell 3 x minus x y end cell equals cell negative 6 y minus 2 end cell row cell x open parentheses 3 minus y close parentheses end cell equals cell negative 6 y minus 2 end cell row x equals cell fraction numerator negative 6 y minus 2 over denominator 3 minus y end fraction end cell row x equals cell fraction numerator up diagonal strike negative 1 end strike open parentheses 6 y plus 2 close parentheses over denominator up diagonal strike negative 1 end strike open parentheses y minus 3 close parentheses end fraction end cell row x equals cell fraction numerator 6 y plus 2 over denominator y minus 3 end fraction end cell row cell g to the power of negative 1 end exponent open parentheses y close parentheses end cell equals cell fraction numerator 6 y plus 2 over denominator y minus 3 end fraction end cell row cell g to the power of negative 1 end exponent open parentheses x close parentheses end cell equals cell fraction numerator 6 x plus 2 over denominator x minus 3 end fraction end cell end table end style$

Jadi, invers dari fungsi $begin mathsize 14px style g left parenthesis x right parenthesis equals fraction numerator 3 x plus 2 over denominator x minus 6 end fraction comma space x not equal to 6 space end style$ adalah $begin mathsize 14px style g to the power of negative 1 end exponent table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell open parentheses x close parentheses end cell end table table attributes columnalign right center left columnspacing 0px end attributes row blank equals blank end table table attributes columnalign right center left columnspacing 0px end attributes row blank blank cell fraction numerator 6 x plus 2 over denominator x minus 3 end fraction end cell end table comma space x not equal to 3. end style$