Page 329 - Calculus Demystified

Final Exam
316
15. The tangent, cotangent, and secant of the angle 3π/4 (measured in
radians) are
√
(a) − 3/2, −1/2, 1
√ √
(b) 1/ 2, 1/ 2, −1
√ √
(c) 2, − 2, 2
√
(d) 1, −1, 3
√
(e) −1, −1, − 2
√
16. The domain and range of the function g(x) = 1 + 2x are
(a) {x : x ≥−1/2} and {x : 0 ≤ x< ∞}
√
(b) {x : x ≥ 1/2} and {x : 2 ≤ x ≤ 2}
(c) {x : x ≤−1/2} and {y :−2 ≤ y< ∞}
(d) {s : 1 ≤ s ≤ 2} and {t : 2 ≤ t ≤ 4}
(e) {x : 0 ≤ x ≤ 2} and {x : 1 ≤ x ≤ 4}
17. The graph of the function y = 1/|x| is
(a) Entirely in the second and third quadrants
(b) Entirely in the first and fourth quadrants
(c) Entirely above the x-axis
(d) Increasing as x moves from left to right
(e) Decreasing as x moves from left to right
2
18. The graph of y = 2x/(1 + x ) includes the points
(a) (0, 1), (2, 4), (3, 3)
(b) (1, 1), (2, 2), (4, 4)
(c) (−1, 1), (1, −1), (3, 6)
(d) (1, 1), (2, 4/5), (−2, −4/5)
(e) (0, 0), (−4, 3), (4, 5)
3
2
19. Let f(x) = x + x and g(x) = x − x. Then
2
x
2
(a) f ◦ g(x) = (x + x) and g ◦ f(x) = (x − x)2x
2
3
2
3
(b) f ◦ g(x) = (x + x) + x, g ◦ f(x) = (x − x) + x
2
3
3
3
2
2
(c) f ◦ g(x) = (x −x) +(x −x) and g ◦ f(x) = (x +x) −(x +x)
2
2
3
3
(d) f ◦ g(x) = (x + x) · (x − x) and g ◦ f(x) = (x + x)/(x − x)
2
3
3
2
(e) f ◦ g(x) = (x + x) + (x − x) and g ◦ f(x) = (x − x) x +x
√
20. Let f(x) = 3 x + 1. Then
3
(a) f −1 (x) = x − 1
√
(b) f −1 (x) = 3 x − 1