Page 36 - Pra U STPM 2022 Penggal 1 - Mathematics (T)

Mathematics Term 1 STPM Chapter 1 Functions

Example 28

2
3
If f(x) = 2x – 9x + 3x + 14, factorise f(x). Sketch the graph of y = f(x). 1
Hence, find the set of values of x such that f(x)  0.
3
Solution: f(x) = 2x – 9x + 3x + 14
2
f(–1) = –2 – 9 – 3 + 14 y
= 0
Hence, (x + 1) is a factor of f(x).
Using long division method, y = f(x)
f(x) = (x + 1)(2x – 11x + 14)
2
= (x + 1)(x – 2)(2x – 7)
At the x-axis, f(x) = 0
i.e. (x + 1)(x – 2)(2x – 7) = 0 x
x = –1, 2 or — –1 0 2 7 _
7
2
2
So the graph of f(x) intersects the x-axis at x = –1, 2 and 7 .
The graph of f(x) is as shown on the right. 2
From the sketch graph of y = f(x),
we see that f(x)  0 if –1 < x < 2 or x  7 .
2
Hence, the set of values of x such that f(x)  0 is
{x : –1 < x < 2 or x  7 }.
2

Example 29

Find the set of values of x such that x . 6 + 1.
x
6
Solution: Given that x . x + 1
6
x – x – 1 . 0
2
x – x – 6
x . 0
(x – 3)(x + 2)
x . 0
Let f(x) = (x – 3)(x + 2)
x
Notice that f(x) changes sign when x passes through x = 3, 0 and –2.
We draw up a table for the sign of f(x) by considering the sign of each factor in
each interval of x, as shown below.
x , –2 –2 , x , 0 0 , x , 3 x . 3
(x + 2) – + + +
x – – + + The sign of f(x)
is obtained by
(x – 3) – – – + multiplying the
f(x) – + – + signs of the 3
factors in each
From the above table, we see that f(x) . 0 or x . 6 x + 1, interval.
when –2 , x , 0 or x . 3.
Hence, the set of values of x is {x : –2 , x , 0 or x . 3}.

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01a STPM Math T T1.indd 33 3/28/18 4:20 PM