Page 27 - Algebra 1

Worked Example 10
Find the domain of x2 x2+3x−4
Solution:
The denominator cannot be 0. So,
(x – 1) (x + 4)
Therefore, the domain is (1, –4)
x2 +3x−4≠0
or x2 + 4x − x − 4
or x(x + 4) – 1(x – 4)
Worked Example 11
Find the range of √49 − 𝑥2
Solution:
The domain of the function is given by (–7, 7) For the range,
y=
Since the range of the function is (0, 7)
√49−𝑥2
y2 =49–x2
yismaximumwhenx=0, y=7
y is minimum when x = 7, y = 0
Worked Example 12
If f(x) = 𝑥+|𝑥|, find the value of f(–3) |𝑥|
Solution:
Putx=–3in 𝑥+|𝑥| |𝑥|
Asx<0,f(x)=|x|wouldbe –x
= –3+|–3| |–3|
= –3−3 = 2 –3
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ALGEBRA