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Stitz-Zeager_College_Algebra_e-book

# X y f x x f x 3 23 2 22 1 8 1 4 8 3 1 8 2 7 1 4 1 2 6

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Unformatted text preview: = 6x − 2 (b) f (x) = 5x − 3 4 + 3x (c) f (x) = 1 − √5 (d) f (x) = − x − 5 + 2 √ (e) f (x) = 3x − 1 + 5 √ (f) f (x) = 5 3x − 1 (g) f (x) = x2 − 10x, x ≥ 5 (h) f (x) = 3(x + 4)2 − 5, x ≤ −4 (i) f (x) = x2 − 6x + 5, x ≤ 3 (j) f (x) = 4x2 + 4x + 1, x < −1 3 (k) f (x) = 4−x x (l) f (x) = 1 − 3x 2x − 1 (m) f (x) = 3x + 4 4x + 2 (n) f (x) = 3x − 6 −3x − 2 (o) f (x) = x+3 2. Show that the Fahrenheit to Celsius conversion function found in Exercise 3 in Section 2.1 is invertible and that its inverse is the Celsius to Fahrenheit conversion function. 3. Analytically show that the function f (x) = x3 + 3x + 1 is one-to-one. Since ﬁnding a formula for its inverse is beyond the scope of this textbook, use Theorem 5.2 to help you compute f −1 (1), f −1 (5), and f −1 (−3). 4. With the help of your classmates, ﬁnd a formula for the inverse of the following. (a) f (x) = ax + b, a = 0 √ (b) f (x) = a x − h + k, a = 0, x ≥ h (c) f (x) = (d) f (x) = ax+b cx+d , a = 0, b = 0, c = 0, d = 0 ax2 + bx + c where a = 0, x ≥ − 2ba . 2x 5. Let f (x) = x2 −1 . Using the techniques in Se...
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