2. A function, f, is called ....if, whenever a + b, then f (a) + f (b). That is, for any two distinct inputs to the function, the outputs are also distinct.

Q: Prove or disprove that if ∇ . F = 0 and ∇ * F = 0, then F = 0

A:

Q: 2. (a) Suppose f is a function with domain [a, b]. If f is an odd function, what can be deduced…

A: Note: As per the bartleby policy we can answer single question with maximum 3 subpart so i am…

Q: 4. Suppose P is the set of people alive today and C is the setof possible eye colors. Let f : P → C…

A: Given :          P is the set of people alive today and C is the set of possible eye colors.…

Q: 7. If a function f, whose domain is all real numbers, is even and if 4 is a zero of f, then is also…

A: Given : if a function f , whose domain is all real numbers is even and if 4 is a zero of f then…

Q: Let f(x, y) = x° /Y Evaluate f(5, 1)

A:

Q: Suppose that f : A → B is a function, C C B and D C B. Prove that Š (C – D) = } (C) - } (D).

A: Solution :-

Q: function is defined as c*x^1 from 1 to 5 and 0 otherwise. What is c?

A:

Q: The following fragment of a train schedule for the New Jersey Transit System defines a function f…

A:

Q: If the domain of the function f is not given, then the set of values of the independent variable for…

A: If the domain of the function f is not given, then the set of values of theindependent variable for…

Q: If f(a) > f(x) in an open interval containing a, x + a, then the function value f(a) is a relative .…

A: Given: If f(a)>f(x) in an open interval containing a, x≠a, then the function value f(a) is a…

Q: 1. Determine if cach relation is a function. b)

A: We are authorized to answer three subparts at a time, since you have not mentioned which part you…

Q: 2. (a) Suppose f is a function with domain a, b). Iff is an odd function, what can be deduced about…

A: (a) We know that , if f is an odd function then    f(-x) = -f(x)  Here given that f is a function…

Q: 1. If f(x) = x + 5 and g(x) = x – 5, (a) f(g(x)) = (b) g(f(x)) (c) Thus g(x) is called an function…

A: Note: According to our answering guidelines we have to solve only one question (if multiple…

Q: 6. Consider these functions from the set of students in a discrete mathematics class. Under what…

A: (a) The students from the set of student if it is assigned to his/ her mobile number is one to one…

Q: Iff: X→ Y is a function and F is a nonempty family of subsets of y, then o(ƒ˜¹ (F¹)) =ƒ˜¹ (0 (F)).

A:

Q: 5. If x1 and x2 are two different inputs of a function f, then f is one-to-one if

A: We know that a function y = f(x) is said to be one to one if for each pair of distinct elements in…

Q: Suppose that the function g is defined as follows. -3 if - 3.5 <xs-2.5 -2 if - 2.5<xs-1.5 g(x) = {…

A: Given function is as below :…

Q: The following fragment of a train schedule for the New Jersey Transit System defines a function f…

A: A train schedule for the New Jersey Transit System defines a function f from towns to times

Q: Suppose f is a function with domain [a, b]. If f is an odd function, what can be deduced about a and…

A: Since solve the first question for you. If you want any specific question to be solved then please…

Q: 5. Suppose f(x) is an odd function. Prove that g(x)=f(x)| is an even function.

A:

Q: Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a functionfrom A to B.…

A: givenA = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a functionfrom A to B

Q: What is the graph of a function f that satisfies the following con- ditions: • f'(x) > 0 on (-00,-1)…

A:

Q: How do you show the image of the intersecction of S and T is a subset of the intersection of the…

A: Let function f from A into B. Let S and T are subset of A. To show that fA∩B⊂fA∩fB. Let y∈fA∩B. To…

Q: Let k(x)=f(x)g(x)h(x). If f(5)=−9,f′(5)=0,g(5)=−3, g′(5)=9,h(5)=−8, and h′(5)=−4, what is k′(5)?

A: Given, k(x)=f(x)g(x)h(x). If f(5)=−9,f′(5)=0,g(5)=−3, g′(5)=9,h(5)=−8and h′(5)=−4

Q: Which value of az is NOT in the domain of the function G(z) - = 28 12-25 -?

A: Use the definition of domain  to find the value of x

Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove the following: f(C) -…

A:

Q: 7) Construct a table of values for the function f(x) = x 1 in the restricted domain (0, 0.5, 1, 1.5,…

A: Or

Q: Let A = {a, b, c, d} and f = { (a, 0), (c, 12), (d, 18), (b, 12) }. Is f a function from A to B ?…

A: Given, A = {a,b,c,d} f = {(a,0) , (c,12) , (d,18) , (b,12)}

Q: If F is a function from A to B and x is an element of A, then F(x) is ________.

A: It is given that F is the function from A to B.It is known that if A and B are sets and F is a…

Q: If f is an even function, then f −1 exists.

A: Consider an even function ,f(x)=x2 For,x=±2,we have f(±2)=4 Hence, given function is not…

Q: 10) Suppose that the functions f and g are defined as follows. fx) = -5x² + 2x g(x) = 3x – 2 Find()…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: y is a function of x, which of the following cannot be true?   A. When x = 3 and x = 7, then y = 2.…

A:

Q: 9. If f (x) = prove that f (xr) is an even function. et -1 2

A: A function f(x) is said to be even if we have f(-x)=f(x)

Q: The following fragment of a train schedule for the New Jersey Transit System defines a function f…

A: From the table, we see that  f(Hamilton Township)=6.27

Q: 10.18. Let A = {w, x, y, z} and B= {r, s,t}.Give an example of a function f: A →B that is neither…

A:

Q: 7. Give an example of two functions h(x) and g(x), such that (h o g) (x) does not exist.

A: we need to find two functions h(x) and g(x), such that (hog)(x) does not exist. Let us take two…

Q: 2. If f(x) is an even function and g(x) is odd function, then a) f(x) g(x) is an function. b) f(x)…

A: Solution:-

Q: 1. Define h(x) = +y7x + 2, for all real numbers x > -. (a) Is h a one – to – one function? Why or…

A: Since not a particular question asked ,as per guidelines solution to only first question is given

Q: Prove that if f(x) and g(x) are both even functions, then h(x) = f(x) + g(x) is an even function.

A: Given that f(x) and g(x) are both even functions.  That means: f(-x)=f(x) and g(-x)=g(x) [by…

Q: If the following arrow diagram defines a function f, then the pre-image of 4 is A B f. A +B 1 3 9 4…

A: Given ,  This arrow diagram defines a function f , then  We have to find the pre - image of 4

Q: Suppose that the function h is defined on the interval (-2.5, 1.5) as follows. -2 if -2.5<x<-1.5 -1…

A: We can answer all the three questions as below.

Q: If c is a domain value for a function f and f(c) = 0, then x = c is called a _____ of thefunction.…

A: c is a domain value and f(c)=0

Q: 2. If f : A → B and g : B→ C are injective functions, then gof: A → C is also injective.

A: We need to prove/disprove statenemt two.

Q: 2. (a) Suppose f is a function with domain a, b. If f is an odd function, what can be deduced about…

A:

Q: On one side are the two parts of the definition of a function f: X -> Y, the definition of…

A: Definition : A function is an equation for which any x that can be plugged into the equation will…

Q: if fi(x) = xand f,(x,) = xf(x»x2) = Is this function independent true false

A: Function is independent if f(x1,x2) = f(x1) f(x2).

Q: The set of all permissible inputs for a function is called the ________, and the set ofall…

A: Fill in the blanks. The set of all permissible inputs for a function is called the ________, and the…

Q: Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) =…

A: Consider the two given functions. fx=2x+1 gx=3x+4   The composition of the functions f and g  is…

Q: 2. (a) Supposef is a function with domain [a, b]. If ƒ is an odd function, what can be deduced about…

A:

Q: (a) Suppose f is a function with domain [a, b]. If f is an odd function, what can be deduced about a…

A: (a) Here, f is an odd function. So, f(-x)=-f(x); all x∈[a,b]. So, if x is in the domain then -x is…