Page 57 - Algebra

Worked Example
Find the domain of
x2
x2+3x−4
Solution:
The denominator cannot be 0. So,
(x – 1) (x + 4)
Therefore, the domain is (−∞, −4) 𝑈 (−4, 1) 𝑈 (1, 4)
x2 + 3x − 4 ≠ 0
orx2 +4x−x−4
or x(x + 4) – 1(x + 4)
Worked Example
Find the range of
Solution:
√49−𝑥2
The domain of the function is given by (–7, 7) For the range,
y=
So, the range of the function is [0, 7]
√49−𝑥2
y2 =49–x2
y is maximum when x = 0, y = 7
y is minimum when x = 7, y = 0
3.3. Types of Functions
• Inverse function
For every function y = f(x), the inverse of the function is given by x = f-1(y)
• Even and odd function
If f(x) is a function of x such that f(-x) = f(x), then f(x) is an even function. For example, f(x) = x2 – 2, f(–x) = (–x)2 – 2
f(–x)=x2 –2
So, f(x) = f(–x), so it’s an even function.
If f(x) is a function of x such that f(x) = – f(x), then f(x) is an odd function. For example, f(x) = x3 + 2x, f(–x) = (–x)3 + 2(– x)
f(–x) = (–x3 –2x)
So, f(x) = –f(x), so it’s an odd function.
• Constant function
If f(x) = c for all x € R, then f(x) is a constant function. For example, f(x) = 12 is a constant function.
• Modulus function
f(x) = |x| for (𝑥, 𝑥≥0 ) –x, x<0
Page 56 of 177
Algebra I & II