1.5.3 Fungsi, SPM Praktis (Soalan Pendek)

1.5.3 Fungsi, SPM Praktis (Soalan Pendek)

Soalan 8:

Cari fungsi songsangan

f (x) = \frac{3 x + 2}{5 x + 3}

Penyelesaian:

\begin{array}{l} f (x) = \frac{3 x + 2}{5 x + 3} \\ katakan y = \frac{3 x + 2}{5 x + 3} \\ y (5 x + 3) = 3 x + 2 \\ 5 x y + 3 y = 3 x + 2 \\ 5 x y - 3 x = 2 - 3 y \\ x (5 y - 3) = 2 - 3 y \\ x = \frac{2 - 3 y}{5 y - 3} \\ f^{- 1} (x) = \frac{2 - 3 x}{5 x - 3} \to \begin{array}{l} tukar y kepada x \\ untuk cari f^{- 1} (x) \end{array} \end{array}

Soalan 9:

(a) Jika f : x → x – 2, cari f ^-1 (5),

(b) Jika f : x \to \frac{x + 9}{x - 5}, x \neq 5, cari f^{- 1} (3) .

Penyelesaian:

(a)

f (x) = x– 2

Katakan y = f ^-1(5)

f (y) = 5

y – 2 = 5

y = 7

oleh itu, f ^-1(5) = 7

(b)

\begin{array}{l} f (x) = \frac{x + 9}{x - 5} \\ katakan y = f^{- 1} (3) \\ f (y) = 3 \\ \frac{y + 9}{y - 5} = 3 \\ y + 9 = 3 y - 15 \\ 2 y = 24 \\ y = 12 \\ ∴ f^{- 1} (3) = 7 \end{array}