f(x) = x² + 3x – 2
g(x)= x + 3
h(x)= 2x – 1
Ditanya:
a.(H•G•F)(x)
b.(H•H•H)(x)
c.(G•G•G)(x)
Diketahui:
f(x) = (x² + 3x – 2)
g(x) = (x + 3)
h(x) = (2x – 1)
(hogof)(x) = h(g(f(x)))
(hogof)(x) = h(g(x² + 3x – 2))
(hogof)(x) = h((x² + 3x – 2) + 3)
(hogof)(x) = h(x² + 3x – 2 + 3)
(hogof)(x) = h(x² + 3x + 1)
(hogof)(x) = 2•(x² + 3x + 1) – 1
(hogof)(x) = (2x² + 6x + 2) – 1
(hogof)(x) = 2x² + 6x + 2 – 1
(hogof)(x) = 2x² + 6x + 1
(hohoh)(x) = h(h(h(x)))
(hohoh)(x) = h(h(2x – 1))
(hohoh)(x) = h(2•(2x – 1) – 1)
(hohoh)(x) = h((4x – 2) – 1)
(hohoh)(x) = h(4x – 2 – 1)
(hohoh)(x) = h(4x – 3)
(hohoh)(x) = 2•(4x – 3) – 1
(hohoh)(x) = (8x – 6) – 1
(hohoh)(x) = 8x – 6 – 1
(hohoh)(x) = 8x – 7
(gogog)(x) = g(g(g(x)))
(gogog)(x) = g(g(x + 3))
(gogog)(x) = g((x + 3) + 3)
(gogog)(x) = g(x + 3 + 3)
(gogog)(x) = g(x + 6)
(gogog)(x) = (x + 6) + 3
(gogog)(x) = x + 6 + 3
(gogog)(x) = x + 9