The following functions all have domain {1, 2, 3, 4, 5} and codomain {1, 2, 3}. For each, determine whetherit is (only) injective, (only) surjective, bijective, or neither injective nor surjective.a. f(n) = (C.1 2 3 4 51Choose an answer: Select an answerb. f(n) = ( 1²(1²345){²2 3 1 22Choose an answer: Select an answerx < 3x > 3Choose an answer: Select an answerî<>

Answered: Image /qna-images/answer/fe931115-7de7-4dee-a015-b0cac87f65c0.jpg

Answered: The following functions all have domain…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Let A = {-7, 0, 7} and B = {t, u, v, w}. Define a function F: A → B by the following arrow diagram: F A B и M. (a) What are the domain and co-domain of F? (Enter your answers in set-roster notation.) domain of F = co-domain of F = (b) F(-7) = F(0) = F(7) =
True or false
suppose m>0 is an integer. How many one-to-one functions are from a set of m elements to a set of m-1 elements?
b. The functions g and h are defined by g: x→x2 – 4 and f: x→. where x is a 2-x real number. i. State the domain of each of the two functions ii. Determine whether or not f is a one -to- one function iii. Find the inverse of the function f c. The functions h and m are defined on the set R of real numbers by h: x→ax +b and m: x → cx -d, where a, b, c and d are constants. If hom=moh, show that (c-1)b = (a-1)d
d) Give an example of a function from A to B that isone-to-one. e) Give an example of a function from A to B that isonto. f) How many functions are there from B to A? Explainbriefly.
Let f be a function from R to R. Without using words of negation, write the meaning of “f is not an increasing function”.
Determine the domain and range of the functions below. a. f(x,y) = |x"/4| for any real numbers x and y where y 0. b. The function that assigns to a bit string the numerical position of the last 0 in the string and it assigns a 0 to a bit string of all 1s.
The function f is graphed below. State the values that fulfill the following requirements. If there are no such values, type DNE. If there are multiple discrete values, separate them with commas. there are a whole interval of values that fulfill the requirement, use interval notation to give all of the values in the interval. Type oo for ∞ and -oo for -∞. Also type U for U. YA (1.5,2) 2- 1.5- 1- (-0.7.0.2) 0.5- 1 -0.5 Where does f have local minimums? What are these local minimum values? the relative minimum is which occurs at x = Where does f have local maximums? the relative maximums occur at a 1.5 -0.5- -1.5- (0.7,0.2) 0.5 1 1.5X (-1.2,-1) Where is f-0? at x = What are the values in the closed interval [-1.2, 1.5] where f undefined? at x = 2+
6. Based on what you know about the multiplicative principle, how many functions f:A- Bare there if |A| = 5 and |B| = 7? How many of those are injective? How many are surjective? Explain your answers.
asap
Determine if these functions are reflexive, symmetric, antisymmetric, and/or transitive. a. {(x, y) | x = ëyû} on the set of real numbersb. {(m, n) | m2 = n2 } on the set of integersc. {(a, b) | classroom a has a larger capacity than classroom b} on the set of classroomsd. {(1, 1), (2, 2), (1, 2), (2, 3), (3, 2), (3, 3)} on the set {1, 2, 3}
Determine the intervals on which the function is concave up or down and find the points of inflection. f(x) = 4x³ — 5x² +8 (Give your answer as a comma-separated list of points in the form (*, *). Express numbers in exact form. Use symbolic notation and fractions where needed.) points of inflection: Determine the interval on which f is concave up. (Give your answer as an interval in the form (*, *). Use the symbol ∞ for infinity, U for combining intervals, and an appropriate type of parenthesis "(",")", "[","]" depending on whether the interval is open or closed. Enter Ø if the interval is empty. Express numbers in exact form. Use symbolic notation and fractions where needed.) x E Determine the interval on which f is concave down.

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