1st Honours Algebra Quick Quiz 1 Click on the correct answer to the question. 1. A function f is a rule which assigns to each element x in the domain of f in the range of f. A. two or more elements B. a unique element C. a transuranic element D. a eunuch's elephant 2. Let f(x) = |x|, the absolute value of x, where the domain and range of f is R. Does f define a function? A. Only on Sundays. B. Yes. C. No. D. It does, in a kind of a way. 3. Is the function in question 2 injective? A. No. B. Yes. C. Only if it's going into your arm. D. Sometimes. 4. Is the function in question 2 surjective? A. Yes. B. No. 5. Complete the definition. A function f is said to be injective if f(x1) equal to f(x2) implies A. x1 is not equal to x2 B. x1 is greater than x2 C. x1 is less than x2 D. x1 is equal to x2 6. If you draw a graph for the function f(x) = 3x + 1 then you will easily see that the function is: A. injective but not surjective B. surjective but not injective C. bijective D. neither injective nor surjective 7. Let f be the function given by f(x) = x5, where both the domain and range of f is R. Then the inverse of the function f is: A. g(x) = 1/x5 B. f does not have an inverse C. g(x) = fifth root of x D. the opposite of the function f 8. Let f(x) = 5x + 3, where both the domain and range of f is R. Then the inverse of f is found to be: A. g(x) = (x - 3)/5 B. g(x) = (x + 3)/5 C. f-1(x) D. f does not have an inverse 9. Let f(x) = 3, where both the domain and range of f is R. Then the inverse of f is found to be: A. g(x) = 1/3 B. g(x) = x - 3 C. f-1(x) D. f does not have an inverse 10. Only one of the following is true for all functions. Which one. A. f and g both surjective then f o g is injective B. f and g both injective then g o f is injective C. f and g both injective then g o f is surjective D. f and g both injective then g o f is bijective 11. If f, g and h are functions, then f o (g o h) = (f o g) o h. To describe this fact we say that A. Composition of functions is commutative B. Functional associativity is compositional C. Functions can be associated with compost D. Composition of functions is associative 12. The pigeonhole principle states that if m objects are distributed among n boxes, where m > n, then at least one box A. has a pigeon in it B. receives at least one object C. receives no objects D. receives at least two objects 13. When there is a bijection from the set of natural numbers to a set X, we say that the set X is A. way big B. countable C. uncountable D. bijective 14. When there is a bijection from the set {1, 2, ..., n} to a set X, where n is a natural number, we say that the set X is A. countable B. infinite C. finite D. settling in 15. An example of an uncountable set is A. the rational numbers B. the set of all finite subsets of the natural numbers C. the real numbers D. the natural numbers If you think I've got an answer wrong, e-mail me at rbreams@vcu.edu so that I can correct it.
Click on the correct answer to the question.
1. A function f is a rule which assigns to each element x in the domain of f in the range of f. A. two or more elements B. a unique element C. a transuranic element D. a eunuch's elephant
2. Let f(x) = |x|, the absolute value of x, where the domain and range of f is R. Does f define a function? A. Only on Sundays. B. Yes. C. No. D. It does, in a kind of a way.
3. Is the function in question 2 injective? A. No. B. Yes. C. Only if it's going into your arm. D. Sometimes.
4. Is the function in question 2 surjective? A. Yes. B. No.
5. Complete the definition. A function f is said to be injective if f(x1) equal to f(x2) implies A. x1 is not equal to x2 B. x1 is greater than x2 C. x1 is less than x2 D. x1 is equal to x2
6. If you draw a graph for the function f(x) = 3x + 1 then you will easily see that the function is: A. injective but not surjective B. surjective but not injective C. bijective D. neither injective nor surjective
7. Let f be the function given by f(x) = x5, where both the domain and range of f is R. Then the inverse of the function f is: A. g(x) = 1/x5 B. f does not have an inverse C. g(x) = fifth root of x D. the opposite of the function f
8. Let f(x) = 5x + 3, where both the domain and range of f is R. Then the inverse of f is found to be: A. g(x) = (x - 3)/5 B. g(x) = (x + 3)/5 C. f-1(x) D. f does not have an inverse
9. Let f(x) = 3, where both the domain and range of f is R. Then the inverse of f is found to be: A. g(x) = 1/3 B. g(x) = x - 3 C. f-1(x) D. f does not have an inverse
10. Only one of the following is true for all functions. Which one. A. f and g both surjective then f o g is injective B. f and g both injective then g o f is injective C. f and g both injective then g o f is surjective D. f and g both injective then g o f is bijective
11. If f, g and h are functions, then f o (g o h) = (f o g) o h. To describe this fact we say that A. Composition of functions is commutative B. Functional associativity is compositional C. Functions can be associated with compost D. Composition of functions is associative
12. The pigeonhole principle states that if m objects are distributed among n boxes, where m > n, then at least one box A. has a pigeon in it B. receives at least one object C. receives no objects D. receives at least two objects
13. When there is a bijection from the set of natural numbers to a set X, we say that the set X is A. way big B. countable C. uncountable D. bijective
14. When there is a bijection from the set {1, 2, ..., n} to a set X, where n is a natural number, we say that the set X is A. countable B. infinite C. finite D. settling in
15. An example of an uncountable set is A. the rational numbers B. the set of all finite subsets of the natural numbers C. the real numbers D. the natural numbers