MAT1514 Assignment 1 (DETAILED ANSWERS 2025 - DISTINCTION GUARANTEED

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