*** Diketahui g(x) = 2/3x+3 + 1/x+1; x ≠ -1. invers fungsi g(x) adalah

*** Diketahui g(x) = 2/3x+3 + 1/x+1; x ≠ -1. invers fungsi g(x) adalah

g(x) = 2 / (3x + 3) + 1 / (x + 1)

= ( 2 + 3 ) / (3x + 3)

= 5 / ( 3x + 3 )

y = 5 / ( 3x + 3 )

3xy + 3y = 5

3y (x + 1) = 5

x + 1 = 5 / 3y

x = ( 5 / 3y ) – 1

x = ( 5 – 3y ) / 3y

g^-1(x) = ( 5 – 3x ) / 3x atau ( 5 / 3y ) – 1

Jawaban:

${g}^{ - 1} (x) = frac{5}{3x} - 1$

Penjelasan dengan langkah-langkah:

Buat lebih simpel

$g(x) = frac{2}{3x + 3} + frac{1}{x + 1}$

$g(x) = frac{2}{3x + 3} + frac{3}{3x + 3}$

$g(x) = frac{5}{3x + 3}$

$y = frac{5}{3x + 3}$

$3xy + 3y = 5$

$3y(x + 1) = 5$

$x + 1 = frac{5}{3y}$

$x = frac{5}{3y} - 1$

${g}^{ - 1} (x) = frac{5}{3x} - 1$