Page 35 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

1
For all x  R, –3 x – 1 2 2 < 0.
3
2
1 Hence, –3x + 2x – 5 , 0 for all x  R.

Alternative Method:
2
(a) h(x) = 2x + 8x + 9
with a = 2, b = 8, c = 9. y
2
2
b – 4ac = 8 – 4(2)(9)
= 64 – 72
= –8 y = h(x)
2
Hence, b – 4 ac , 0 and the graph of y = h(x) does not intersect the x-axis.
x
Since a . 0, the graph of y = h(x) is always above the x-axis. 0
2
Hence, 2x + 8x + 9 . 0 for all x  R.
2
(b) k(x) = –3x + 2x – 5
with a = –3, b = 2 , c = –5.
2
2
b – 4ac = 2 – 4(–3)(–5) y
= 4 – 60 x
0
= –56
y = k(x)
2
Hence, b – 4ac , 0 and the graph of y = k(x) does not intersect the x-axis.
Since a , 0, the graph of y = k(x) is always below the x-axis.
2
Hence, –3x + 2x – 5 , 0 for all x  R.
Example 27

2
Find the set of values of x which satisfy the inequality 2x + x . 3.
2
Solution: Given 2x + x . 3
2
or 2x + x – 3 . 0 y
(2x + 3)(x – 1) . 0
2
f(x) = 2x + x – 3
Consider the graph of the function
f(x) = (2x + 3)(x – 1) x
3 _ 0 1
–
At the points of intersection with the x-axis, 2
(2x + 3)(x – 1) = 0
Hence 2x + 3 = 0 or x – 1 = 0
3

x = – or x = 1
2
3
From the graph of f(x), f(x) . 0 if x , – or x . 1.
2
2
Hence, the range of values of x which satisfy the inequality 2x + x . 3
3
is x , – or x . 1.
2
3
The solution set of the inequality is {x : x , – or x . 1}.
2

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01a STPM Math T T1.indd 32 3/28/18 4:20 PM