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Stitz-Zeager_College_Algebra_e-book

# We proceed as before nding intercepts testing for

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Unformatted text preview: g − h)(x) f (x) g iv. (f h)(x) iii. v. (g + h)(x) h vi. (x) g (x) 1.6 Function Arithmetic 4. Find and simplify the diﬀerence quotient (a) (b) (c) (d) (e) (f) f (x) = 2x − 5 f (x) = −3x + 5 f (x) = 6 f (x) = 3x2 − x f (x) = −x2 + 2x − 1 f (x) = x3 + 1 2 (g) f (x) = x 3 61 f (x + h) − f (x) for the following functions. h 3 (h) f (x) = 1−x x (i) f (x) = x−9 √3 (j) f (x) = x (k) f (x) = mx + b where m = 0 (l) f (x) = ax2 + bx + c where a = 0 Rationalize the numerator. It won’t look ‘simpliﬁed’ per se, but work through until you can cancel the ‘h’. 62 Relations and Functions 1.6.2 Answers 1. (a) (b) i. (f + g )(4) = 16 i. (f + g )(x) = √ ii. (g −h)(7) = 118 7 x + x + 10 h g iv. Domain: [0, ∞) 1 x Domain: (−∞, 0) ∪ (0, ∞) 1 iii. (f h)(x) = √ x Domain: (0, ∞) (b) i. (f + g )(4) = 23 (x) = iv. h g (3) = 1 39 1 x(x + 10) Domain: (−∞, −10) ∪ (−10, 0) ∪ (0, ∞) g v. (x) = x(x + 10) h Domain: (−∞, 0) ∪ (0, ∞) 1√ vi. (h − f )(x) = − x x...
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