MAT1514 Assignment 1 (DETAILED ANSWERS 2025 - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED Answers, guidelines, workings and references ,... Question 1 Given f (x) = 3x2 − 4x + 7 and g(x) = x2 + 1. Find and simplify the following: apm1514 1. (g f )(x) (4) 2. (g − f )(x) (2) 3. g f (x) (4) 4. g−1(x) (3) [13 marks] 2 Downloaded by Corona Virus () lOMoARcPSD| MAT1514/101/0/2025 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)mat1511 mat1512 (b) y = 3(x + 2)2 − 5 (1) (c) x2 − y2 = 9 (1) 3. Determine whether the lines y = 5 mat1513 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. mat1501 mat1503 • The function contains the point (2,−5). (5) 4. Find the quotient and remainder if 4x3 + 7x2 − 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
Quality you can trust: written by students who passed their tests and reviewed by others who've used these notes.
No worries! You can instantly pick a different document that better fits what you're looking for.
No subscription, no commitments. Pay the way you're used to via credit card and download your PDF document instantly.
“Bought, downloaded, and aced it. It really can be that simple.”
