Diketahui fungsi f open parentheses 3 x minus 1 close parentheses equals x minus 1 dan fungsi g open parentheses x close parentheses equals 18 x squared minus

f(3x - 1) = x - 1
g(x) = 18x² - 3x + 1

Ditanya : (gof)(x)

f(3x - 1) = x - 1
Misalkan y = 3x - 1
Maka, x = (y + 1)/3

f(y) = (y + 1)/3 - 1
f(y) = (y + 1)/3 - 3/3
f(y) = (y - 2)/3
Atau
f(x) = (x - 2)/3

(gof)(x)
= g(f(x))
= 18(f(x))² - 3(f(x)) + 1
[tex] = 18(\frac{x-2}{3})^2 - 3(\frac{x - 2}{3}) + 1 \\ = 18(\frac{x^2-4x+4}{9}) - (x - 2) + 1 \\ = 2(x^2 - 4x + 4) - x + 2 + 1 \\ = 2x^2 - 9x + 11 [/tex]