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1.3a Fungsi Gubahan

Jika fungsi f : X → Y,

dan fungsi g : Y → Z,

maka, fungsi gubahan gf: X → Z

Soalan 1:

Diberi fungsi f : x → 2x + 5 dan g : x→ x² – 1, cari gf (2)

Penyelesaian:

f (x) = 2x + 5

f (2) = 2(2) + 5 = 9

gf (2) = g [f (2)] = g (9)

g(x) = x²– 1

gf(2) = g(9) = 9² – 1 = 80

Soalan 2:

Jika f : x → x + 5 dan g : x → x² + 2x + 3, cari
(a) nilai gf (2),
(b) nilai fg (2 ),
(c) fungsi gubahanfg,
(d) fungsi gubahan gf,
(e) fungsi gubahan g²,
(f) fungsi gubahan f ².

Penyelesaian:

Pembetulan bagi (c)

\begin{array}{l} f g (x) = f (x^{2} + 2 x + 3) \\ = (x^{2} + 2 x + 3) + 5 \\ = x^{2} + 2 x + 3 + 5 \\ = x^{2} + 2 x + 8 \end{array}

Pembetulan bagi (e)

\begin{array}{l} g^{2} (x) = g g (x) \\ = g (x^{2} + 2 x + 3) \\ = {(x^{2} + 2 x + 3)}^{2} + 2 (x^{2} + 2 x + 3) + 3 \\ = x^{4} + 2 x^{3} + 3 x^{2} + 2 x^{3} + 4 x^{2} + 6 x \\ + 3 x^{2} + 6 x + 9 \\ = x^{4} + 4 x^{3} + 10 x^{2} + 12 x + 9 \end{array}