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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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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