Question

mtk

Misalkan diketahui f(x) = 3x – 1, g(x) = x2+1 dan h(x) = 1 - x.
Tentukan : goh2 Buktikan apakah f o g o h x =. g o f o h(x) ?​

Answer 1

Jawab:

f(x) = 3x - 1

g(x) = x² + 1

h(x) = 1 - x

(g o h)(x) = g(h(x))

(g o h)(x) = g(1 - x)

(g o h)(x) = (1 - x)² + 1

(g o h)(x) = x² - 2x + 1 + 1

(g o h)(x) = x² - 2x + 2

(f o g o h)(x) = (g o f o h)(x)

f(g(h(x))) = g(f(h(x)))

f(g(1-x)) = g(f(1-x)

f((1-x)² + 1) = g(3(1-x) - 1)

f(x² - 2x + 1 + 1) = g(3 - 3x - 1)

f(x² - 2x + 2) = g(2 - 3x)

3(x² - 2x + 2) - 1 = (2 - 3x)² + 1

3x² - 6x + 6 - 3 = 9x² - 12x + 4 + 1

3x² - 6x + 3 ≠ 9x² - 12x + 5

Maka (f o g o h)(x) ≠ (g o f o h)(x)