An easy help for students

2. How to evaluate an
algebraic formula
• RECAP
• Example: given that 𝐹 =
𝑚(𝑣−𝑢)
𝑟2 , find the value of f where
m = 80, v = 20 , u = 10 and r = 5.
Solution: we substitute all given values of the letters accordingly.
𝐹 =
80(20−10)
52
𝐹 =
80(10)
25
𝐹 =
800
25
hence, we get F = 32
This concept is a base for
further discussion

3. Functions of higher order
We already have studied
• Linear function 𝒇(𝒙) = 𝒎𝒙 + 𝒄
• Quadratic function 𝒇(𝒙) = 𝒂𝒙 𝟐 + 𝒃𝒙 + 𝒄
• There are more functions according to the degree of variable.
Here we are going to evaluate different functions for the values given in the question.
Example: Given that 𝒇 𝒙 = 𝟑𝒙 𝟐 − 𝟏, find 𝒇 𝟐
𝟏
𝟑
Solution: Substitute 𝐱 = 𝟐
𝟏
𝟑
in the function and solve it.
𝒇 𝟑
𝟏
𝟐
= 𝟑 𝟑
𝟏
𝟐
𝟐
− 𝟏 𝒇 𝟑
𝟏
𝟐
= 𝟑
𝟕
𝟑
𝟐
− 𝟏 𝒇 𝟑
𝟏
𝟐
= 𝟑
𝟒𝟗
𝟗
− 𝟏
𝒇 𝟑
𝟏
𝟐
=
𝟒𝟗
𝟑
− 𝟏 =
𝟒𝟔
𝟑
= 𝟏𝟓
𝟏
𝟑
(simplified answer)
Activity: D-3 Exercise 2A Q1 & 2

4. PROBLEMS INVOLVING FUNCTIONS AND
SIMULTANEOUS EQUATIONS
Example: Given that the function h 𝒙 = 𝒄𝒙 + 𝒅 and h(2) = 6 and h(7) = 16,
find the value of h and of d.
Solution: 𝒉 𝟐 = 𝟐𝒄 + 𝒅 = 𝟔 (1)
𝒉 𝟕 = 𝟕𝒄 + 𝒅 = 𝟏𝟔 (2)
By subtracting equation (1) from (2), we get
𝟓𝒄 = 𝟏𝟎
c = 𝟐
Substituting c = 𝟐 into equation 1
𝟐(𝟐) + 𝒅 = 𝟔
𝟒 + 𝒅 = 𝟔
Activity : Ex 2A Q 3, 4 & 5