Stitz-Zeager_College_Algebra_e-book

# F h25 ii g h1 6 i f g x 2x2 3x

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Unformatted text preview: − = = = = 3x − 1 (6x2 − 2x) x simplify complex fractions 58 Relations and Functions 3x − 1 − 1) factor = X \$1 (3x \$\$ \$\$− 1) \$ 2x2\$\$− \$ (3x \$ 1) cancel = 1 2x2 = 2x2 (3x To ﬁnd the domain, we consider the ﬁrst step after substitution: 1 x 6x2 − 2x 3− 1 To avoid division by zero in the ‘little’ fraction, x , we need x = 0. For the ‘big’ fraction we 2 − 2x = 0 and solve: 2x(3x − 1) = 0 and get x = 0, 1 . Thus we must exclude x = 1 as set 6x 3 3 well, resulting in a domain of (−∞, 0) ∪ 0, 1 ∪ 1 , ∞ . 3 3 We close this section with concept of the diﬀerence quotient of a function. It is a critical tool for Calculus and also a great way to practice function notation.2 Definition 1.6. Given a function, f , the diﬀerence quotient of f is the expression: f (x + h) − f (x) h Example 1.6.2. Find and simplify the diﬀerence quotients for the following functions 1. f (x) = x2 − x − 2 2. g (x) = 3 2x + 1 Solution. 1. To ﬁnd f (x + h), we replace every occurrence of x in the formula f (x)...
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