MAT1512 ASSIGNMENT 1 WORKED SOLUTIONS 2026

2026

MAT1512 – CALCULUS I
Assignment 01 -
Solutions
DUE DATE : 26 MAY 2026




1

, Question 1
Given

𝑥 2 − 5𝑥 + 6
𝑓(𝑥) =
𝑥2 − 4

a) Determine the domain of 𝑓.
𝑥 2 − 4 ≠ 0 ⟹ 𝑥 ≠ ±2
∴ 𝐷𝑜𝑚𝑎𝑖𝑛 = ℝ \ {−2, 2}

b) Simplify 𝑓(𝑥) where possible.

𝑥 2 − 5𝑥 + 6
𝑓(𝑥) =
𝑥2 − 4
(𝑥 − 3)(𝑥 − 2)
𝑓(𝑥) =
(𝑥 − 2)(𝑥 + 2)

𝑥−3
𝑓(𝑥) = , 𝑥 ≠ −2
𝑥+2


c) Determine lim 𝑓(𝑥) and state the type of discontinuity at 𝑥 = 2.
𝑥→2

𝑥 2 − 5𝑥 + 6
lim 𝑓(𝑥) = lim
𝑥→2 𝑥→2 𝑥2 − 4
𝑥−3
lim 𝑓(𝑥) = lim
𝑥→2 𝑥→2 𝑥 + 2

2−3 1
lim 𝑓(𝑥) = =−
𝑥→2 2+2 4

⇒ Removable dicontinuity


Question 2
Let
1
𝑓(𝑥) = , 𝑔(𝑥) = √2𝑥 − 3
𝑥−1

a) Determine 𝑓𝜊𝑔(𝑥)

(𝑓𝜊𝑔)(𝑥) = 𝑓(𝑔(𝑥))

1
(𝑓𝜊𝑔)(𝑥) =
√2𝑥 − 3 − 1

2