1.5.8 Fungsi, SPM Praktis (Soalan Pendek)

Soalan 22 (3 markah):
Rajah menunjukkan graf bagi fungsi f : x → |1 – 2x| untuk domain –2 ≤ x ≤ 4.

Rajah

Nyatakan
(a) objek bagi 7,
(b) imej bagi 3,
(c) domain bagi 0 ≤ f(x) ≤ 5.

Penyelesaian:
(a)
Objek bagi 7 ialah 4.

(b)
f (x) = |1 – 2x|
f (3) = |1 – 2(3)|
= |1 – 6|
= |–5|
= 5

Imej bagi 3 ialah 5.

(c)
|1 – 2x| = 5
1 – 2x = ±5
Diberi apabila f(x) = 5, x = –2.

Apabila f(x) = –5
1 – 2x = –5
2x = 6
x = 3

Domain: –2 ≤ x ≤ 3.

Soalan 23 (4 markah):
Diberi fungsi g : x → 2x – 8, cari
$\begin{array}{l}\left(\text{a}\right)g^{-1}\left(x\right),\\ \left(\text{b}\right)\text{ nilai }p\text{ dengan keadaan }{g}^2\left(\frac{3p}{2}\right)=30.\end{array}$

Penyelesaian:
(a)
$\begin{array}{l}\text{Katakan }y=g\left(x\right)\\ =2x-8\\ 2x-8=y\\ 2x=y+8\\ x=\frac{y+8}{2}\\ \text{Maka, }{g}^{-1}\left(x\right)=\frac{x+8}{2}\end{array}$

(b)
$\begin{array}{l}g\left(x\right)=2x-8\\ g^2\left(x\right)=g\left[g\left(x\right)\right]\\ =g\left(2x-8\right)\\ =2\left(2x-8\right)-8\\ =4x-16-8\\ =4x-24\\ g^2\left(\frac{3p}{2}\right)=30\\ 4\left(\frac{3p}{2}\right)-24=30\\ 6p=54\\ p=9\end{array}$