Functions
Grade 12
1- [8marks]
Given 𝒇(𝒙) = 𝟐𝒙 + 𝟏 𝒂𝒏𝒅 𝒈(𝒙) = 𝟑𝒙 − 𝟓
where 𝒙 ∈ 𝑹. Find the following:
a) 𝑔𝑓(−2)
𝑏) 𝑓𝑔(7)
c) 𝑓 −1 (−5)
d) 𝑓𝑔𝑓(𝑥)
2- Find the largest possible domain of each the following functions:
a) √−𝑥
1
b ) 1+
√𝑥
c) √𝑥 − 4
d) √(𝑥 − 1)(𝑥 − 4)
3- Find the largest possible domain of each the following functions:
a) √𝑥
b) √𝑥 2 − 7𝑥 + 12
c) √𝑥 3 − 8
1
b) (𝑥−1)(𝑥−2)
c)
1
√𝑥−2
[6marks]
1
d) 𝑥−2
4- Find the largest possible domain of each the following functions:
a) √−𝑥
[6marks]
[6marks]
d) √4 − 𝑥
5- For all real values of x find the range of each of the following functions: [6marks]
a) 𝑦 = 𝑥 2 + 8𝑥 − 4
b) 𝑦 = (𝑥 + 3)2 − 7
6- For all real values of x find the range of each of the following functions: [6marks]
a) 𝑦 = 𝑥 2 + 16𝑥 + 8
b) 𝑦 = (𝑥 + 5)2 − 2
7- Find the range of each of the following functions for all reel values of x
[6marks]
a) 𝑓(𝑥) = 𝑥 2 + 4
b) 𝑓(𝑥) = (𝑥 − 1)2 + 6
8- Find the range of each of the following functions for all reel values of x
[6marks]
a) 𝑓(𝑥) = −(1 − 𝑥)2 + 7
b) 𝑓(𝑥) = 3(𝑥 + 5)2 + 2
9- These functions are each defined for the given domain. Find their ranges [6marks]
a) 𝑓(𝑥) = 2𝑥 𝑓𝑜𝑟
0≤𝑥≤8
b) 𝑓(𝑥) = 3 − 2𝑥 𝑓𝑜𝑟
−2≤𝑥 ≤2
c) 𝑓(𝑥) = 𝑥 2 − 2 𝑓𝑜𝑟
− 5 ≤ 𝑥 ≤ −2
10-These functions are each defined for the given domain. Find their ranges [6marks]
a) 𝑓(𝑥) = 2𝑥 + 4 𝑓𝑜𝑟
0≤𝑥≤8
b) 𝑓(𝑥) = 5 − 3𝑥 𝑓𝑜𝑟
−2≤𝑥 ≤2
c) 𝑓(𝑥) = 𝑥 2 + 1 𝑓𝑜𝑟
−1≤𝑥 ≤4
11- Find the inverse of each of the following one-to-one functions
[6marks]
5
a) 𝑦 = 𝑥−1
b) 𝑦 = 𝑥 2 − 6𝑥 + 9
12-Find the inverse of each of the following one-to-one functions
a) 𝑦 =
2𝑥+7
3
b) 𝑦 = 𝑥 2 − 4𝑥 + 6
[6marks]
13- [8marks]
a) Find the inverse 𝑓 −1 of 𝑓(𝑥) =
b) Draw 𝑦 =
2𝑥+7
3
2𝑥+7
3
c) hence draw the inverse 𝑓 −1 on the same diagram