198 Chapter 2 Linear Equations in Two Variables and Functions Finding the Domain of a Function Example 6 g1t2 k1t2 t2 3t 1t 4 c. d. Solution: a. will not be a real number when the denominator is zero, that 12 (( Write the domain in interval notation. a. b. 6 5 4 3 2 1 0 1 2 3 4 5 6 is, when The value x must be excluded from the domain. 12 2x 1 0 2x 1 x 1 2 f 1x2 x 7 2x 1 h1x2 x 4 x2 9 f1x2 x 7 2x 1 Answers 18. 1 , 92 ´ 19, 2 19. 1, 2 32,20. 2 12 21. , b. For the quantity is greater than or equal to 0 for all real numbers x, and the number 9 is positive.The sum must be positive for all real numbers x.The denominator will never be zero; therefore, the domain is the set of all real numbers. Interval notation: 6 5 4 3 2 1 0 1 2 3 4 5 6 1, 2 c. The function defined by will not be a real number when the radicand is negative.The domain is the set of all t values that make the radicand greater than or equal to zero: t 4 6 5 4 3 2 1 0 1 2 3 4 5 6 Interval notation: 34, 2 g1t2 t2 3t d. The function defined by has no restrictions on its domain because any real number substituted for t will produce a real number.The domain is the set of all real numbers. Interval notation: Skill Practice Write the domain in interval notation. 18. f 1x2 2x 1 19. k 1x2 5 x 9 4x2 1 20. g1x2 1x 2 21. h 1x2 x 6 6 5 4 3 2 1 0 1 2 3 4 5 6 1, 2 t 4 0 k1t2 1t 4 x2 9 h1x2 x2 x 4 x2 9 Interval notation: a, 1 2 b ´ a1 2 , b
miller_intermediate_algebra_4e_ch1_3
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