Page 67 - Calculus Demystified

54
(a) θ = π/24 CHAPTER 1 Basics
(b) θ =−π/3
(c) θ = 27π/12
(d) θ = 9π/16
(e) θ = 3
(f) θ =−5
16. Convert each of the following angles from degree measure to radian
measure.
(a) θ = 65 ◦
(b) θ = 10 ◦
(c) θ =−75 ◦
(d) θ =−120 ◦
(e) θ = π ◦
(f) θ = 3.14 ◦
17. For each of the following pairs of functions, calculate f ◦ g and g ◦ f .

2
(a) f(x) = x + 2x + 3 g(x) = (x − 1) 2
√ √
3
2
(b) f(x) = x + 1 g(x) = x − 2
2
2
(c) f(x) = sin(x + 3x ) g(x) = cos(x − x)
(d) f(x) = e x+2 g(x) = ln(x − 5)
2
2
(e) f(x) = sin(x + x) g(x) = ln(x − x)
(f) f(x) = e x 2 g(x) = e −x 2
(g) f(x) = x(x + 1)(x + 2) g(x) = (2x − 3)(x + 4)
18. Consider each of the following as functions from R to R and say whether
the function is invertible. If it is, find the inverse with an explicit formula.
3
(a) f(x) = x + 5
2
(b) g(x) = x − x
√
(c) h(x) = (sgn x) · |x|, where sgn x is +1if x is positive, −1if x is
negative, 0 if x is 0.
5
(d) f(x) = x + 8
(e) g(x) = e −3x
(f) h(x) = sin x
(g) f(x) = tan x
2
(h) g(x) = (sgn x) · x , where sgn x is +1if x is positive, −1if x is
negative, 0 if x is 0.
19. For each of the functions in Exercise 18, graph both the function and its
inverse in the same set of axes.