Question 1 (CAS FREE)

Let 𝑓: [0, ∞) → 𝑅, 𝑓(𝑥) = √𝑥 + 1

a. State the range of f.

b. Let 𝑔: (−∞, 𝑐] → 𝑅, 𝑔(𝑥) = 𝑥2 + 4𝑥 + 3. Find the largest value of c for which the

composite function : 𝑓(𝑔(𝑥)) is defined.

c. Evaluate: 𝑓(𝑔(−10))

d. Determine the range of 𝑓(𝑔(𝑥)).

e. Let ℎ: 𝑅 → 𝑅, ℎ(𝑥) = √𝑥2 + 3 . Determine the range of the composite function: 𝑓(ℎ(𝑥))

ASSIGNMENT ON CHAPTER 1

Question 2 (CAS FREE)

The rule for the function h is ℎ(𝑥) = 2𝑥3 + 1. Find the rule for the inverse function ℎ−1

Question 3 (CAS Free)

If the function 𝑓 has the rule: 𝑓(𝑥) = √𝑥2 − 9 and the function g has the rule 𝑔(𝑥) = 𝑥 + 5,

a. find integers c and d such that : 𝑓(𝑔(𝑥)) = √(𝑥 + 𝑐)(𝑥 + 𝑑)

b. Determine the maximal domain of 𝑓(𝑔(𝑥))

Question 4 (CAS FREE)

Let 𝑓: 𝑅+ → 𝑅, 𝑓(𝑥) =1

𝑥2

a. Find 𝑔(𝑥) = 𝑓(𝑓(𝑥))

b. Evaluate 𝑔−1(16) where 𝑔−1 is the inverse function of 𝑔.

Question 5 (CAS FREE)

Question 6 (CAS FREE)

Question 7 (CAS FREE)

MULTIPLE CHOICE (For all Multiple Choice Questions, CAS is allowed)

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14