![MNG3701 Assignment 01 Semester 01 2025 Answers [Due Date : 13 March 2025]](https://studypass.co.za/wp-content/uploads/2025/01/cover-page-300x300.jpg)
Description
MAT1514 Assignment 1 Semester 1 | Due April 2025. All questions answered. This assignment covers Chapters 1, 2, and 3 of the prescribed book and contributes to your year
mark. No calculators may be used.
Question 1
Given
f (x) = 3×2 − 4x + 7
and
g(x) = x2 + 1.
Find and simplify the following:
1. (g f )(x) (4)
2. (g − f )(x) (2)
3.
g
f
(x) (4)
4. g−1(x) (3)
[13 marks]
Question 2
1. Use the graph shown below to determine the intervals on which the function is increasing,
decreasing, or constant. (3)
2. Determine whether the following relations are functions or not:
(a) {(1, 2), (3,−1), (−2, 3), (1,−3)} (1)
(b) y = 3(x + 2)2 − 5 (1)
(c) x2 − y2 = 9 (1)
3
3. Determine whether the lines y = 5
3x +2 and 7x −2y = 4 are parallel, perpendicular, or neither.
(4)
[10 marks]
Question 3
1. If f (x) =
x + 2
x − 3
, evaluate f (−2i ). (4)
2. Find the inverse of the function f (x) = 4x + 5. (5)
3. Given the following information about a polynomial function, find the function:
• The function has a zero of multiplicity 2 at x = −1 and another zero at x = 4.
• The function contains the point (2,−5). (5)
4. Find the quotient and remainder if 4×3 + 7×2 − x + 2 is divided by 2x − 1. (4)
5. Find the domain of f (x) =
3
5x − 4
and express your answer in interval notation. (4)
[22 marks]
Total: 45 marks
4
Paige T (verified owner) –
Good
PreciousNgc –
Very Detailed