MATH
A1_f2015.pdf

# A1_f2015.pdf - MATH 1500 D01/D02 Fall 2015 Assignment 1...

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MATH 1500 D01/D02 Fall 2015 Assignment 1 SHOW ALL WORK to get full marks. Leave answers as exact answers. For example, leave it as 1 { 7 as opposed to 0 . 142857 . Word problems should have sentence answers with units. This assignment covers sections 1.1, 1.3, 1.5, 1.6, 2.1, 2.2, and 2.3. 1. For the following functions, simplify f p a ` h q ´ f p a q h as much as possible. (a) [4] f p x q “ x 2 ` 6 x ´ 4 (b) [4] f p x q “ x ` 1 x ´ 1 2. For the function f defined by f p x q “ x 2 ´ 3 : (a) [3] Find an interval (as large as possible) such that f is one–to–one. (b) [4] Find the inverse of f on the interval from part (a). (c) [3] State the domain and range of f and f ´ 1 using the restriction from part (a). 3. Solve the following equations. (a) [4] log 3 x ` log 3 p 2 x ` 1 q “ 1 (b) [5] ` 3 ? 2 ˘ x ` 10 2 x 2 (c) [3] e x 2 e x ` 6 1 4. (a) [4] Sketch the graph f p x q “ \$ & % p x ` 1 q 2 x ă ´ 1 ´ x ´ 1 ď x ă

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