ALR - A.Y. 2016-17 - Exercises
Lecture 7 and 8
1. Consider f (x) =
√
x and g(x) = x2 , for x ≥ 1. Which sentence is TRUE
(A) f (x) ≥ g(x)
(B) f (x) ≤ g(x)
(C) f (x) ≤ 1
(D) g(x) ≤ 1
2. Consider f (x) = x3 and g(x) = x2 , for x ≥ 1. Which sentence is TRUE
(A) f (x) ≥ g(x)
(B) f (x) ≤ g(x)
(C) f (x) ≤ 1
(D) g(x) ≤ 1
3. Consider f (x) = x3 and g(x) = x2 , for 0 < x < 1. Which sentence is TRUE
(A) f (x) ≥ g(x)
(B) f (x) ≤ g(x)
(C) f (x) ≤ 1
(D) g(x) ≤ 1
4. Consider f (x) = x3 and g(x) = ex . Which sentence is TRUE
(A) f (x) ≥ g(x)
(B) f (x) ≤ g(x)
(C) f (x) ≤ 1
(D) All the previous are wrong
5. Consider f (x) = x3 and g(x) = e−x . Which sentence is TRUE
(A) The graphs of f and g do not intersect
(B) The graph of g intersects the x-axis at a unique point
(C) The graphs of f and g intersect at one point
(D) The previous are all wrong
6. Consider f (x) = e−x . Which sentence is WRONG
(A) f (0) = 1
(B) f (1) = 0
(C) f (x) > 0 for all x
(D) f (1) = 1/e
7. Consider f (x) = ln(x + 1). Which sentence is WRONG
(A) Df = (−1, +∞)
(B) Rf = R
(C) f (x) < 0 for all x < 1
(D) f (e − 1) = 1
8. Consider f (x) = ln(x) and g(x) = ex , for x > 0. Which sentence is WRONG
(A) f is the inverse of g
(B) f (g(x)) = x
(C) g(f (x)) = x
(D) f (x)/g(x) = x
9. If log10 x = −2, then x is worth:
(A) 1/10
(B) 1/100
(C) 10
(D) 20
10. If ex = 2, then x is worth:
(A) ln(2)
(B) 2
(C) e2
(D) 1/2
11. Find the set of solutions to (1/2)x < 2
(A) x > −1
(B) x < −1
(C) x < −1/2
(D) x < −2
12. Find the set of solutions of e2x ≤ 4.
(A) x ≤ ln 3
(B) x ≤ ln 2
(C) x ≤
8
3
(D) x ≤ ln 8
13. Find the set of solutions of
√
3
x ≤ 2.
(A) x ≤ 2
(B) x ≤ ln 2
(C) x ≤ 8
(D) x ≥ 8
14. Find the set of solutions of x1/3 ≥ 10.
(A) x ≤ 3
(B) x ≤ ln 3
(C) x ≤ 1000
(D) x ≥ 1000
15. Find the set of solutions of ln(x + 1) ≥ ln(2).
(A) x ≤ 2
(B) x ≤ ln 2
(C) x ≤ 1
(D) x ≥ 1
16. Find the set of solutions of ln(x + 1) ≤ ln(2).
(A) x ≤ 2
(B) x ≤ ln 2
(C) x ≤ 1
(D) −1 < x ≤ 1