Functions - Chapter 1 PDF
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This document contains exercises on solving functions, inequalities and equations. The document includes multiple exercises.
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# Functions - Chapter 1 ## Exercise 1: Solve each of the following inequalities **1.** * a. 2x + 5 > 3x - 7 => x ∈ (-∞, 12) * b. x - 8 > 5x + 3 * c. 3 ≤ (2x - 3)/5 < 7 * d. 3(1-x) ≤ 6 * e. x² - x - 6 < 0 * f. x² + 4x + 3 ≥ 0 * g. x² - 4x - 17 ≤ 4 * h. x(3x - 1) ≤ 4 * i. x(2x + 3...
# Functions - Chapter 1 ## Exercise 1: Solve each of the following inequalities **1.** * a. 2x + 5 > 3x - 7 => x ∈ (-∞, 12) * b. x - 8 > 5x + 3 * c. 3 ≤ (2x - 3)/5 < 7 * d. 3(1-x) ≤ 6 * e. x² - x - 6 < 0 * f. x² + 4x + 3 ≥ 0 * g. x² - 4x - 17 ≤ 4 * h. x(3x - 1) ≤ 4 * i. x(2x + 3) ≥ 5 * j. (x+1)/(2x - 3) ≥ 2 * k. x - 5 < 3x + 1 ≤ -x + 2 * l. 3x ≤ x + 4 ≤ 2x + 5 * m. x³ > x * n. -3x / (x² - 9) < 0 * o. x² > 3 **2.** Solve each of the following inequalities: * a. 1/(x - 2) ≥ 3/(x + 1) * b. 2/(2x + 3 ) ≤ 2/(x - 5) * c. | x + 3| < 0.01 * d. |x - 4| ≤ 0.03 * e. |x + 2| ≥ 0.001 * f. |2x + 5| < 4 * g. | 6 - 5x| ≤ 3 * h. |3x-7| ≥ 5 * i. |- 11 - 7x| > 6 * j. |x²-7| < 2 * k. | x² - 4 | > 3 * l. | x - 2 | > | 2x - 1 | * m | (x - 1)/(x+1) | ≥ 1 * n. 0 < |x - 2| < 1 * o. |x - 2| ≤ 0 * p. |x + 2| < |3x + 2| * q. |x - 3| > |2x + 1| ## Exercise 3: Solve each of the following equations * a. |7x| = 4 + x * b. |x + 1| - |x| = 20 * c. |x - 3|² - 4|x - 3| = 12
