Dik : fungsi g(x) = 2x + 1 (fog)(x) = x^2 + x tentukan fungsi f(x)

jawab

g(x) = 2x + 1

fog(x) = x² + x
f{ g(x)} = x² + x
f(2x+1) = x² + x
2x + 1= a
2x = a -1
x = 1/2 (a - 1)

f(a) = { 1/2 ( a - 1) }² + 1/2 ( a- 1)
f(a) = 1/4 (a²- 2a + 1) + 1/2 a - 1/2
f(a) = 1/4 a² -1/2 a + 1/4 + 1/2 a - 1/2
f(a) = 1/4 a² - 1/4
f(a) = 1/4 (a² - 1)
f(x) = 1/4 (x² - 1)