h4 .Which of the following families of real functions are algebras of functions? (For each, either show it is an algebra of functions, or else identify a necessary property that is not satisfied.) i. Polynomials of degree at most 2. (That is, polynomials of the form ax2 +bx+c, where any or all of a, b, c may be 0.) ii. Functions f such that f(x) ≤ 6. iii. Functions f that are everywhere defined, and that are continuous at the point c = 2.

Q: Which of the following expressions has a domain that is a subset of the domain (i.e. set of all…

A: We can find the domain of each function and then find the answer.

Q: Refer to the following functions: p(x)=x²+2x-15 x+1 q(x) -- r(x) -√7x Which of the following…

A: Solution :-

Q: 5. Find the V.A. and H.A. of the function 6-9x Sex a). f(x) : b). f (x) : 2x+5 2ex-1

A: Vertical asymptotes: The line x=L is a vertical asymptote of the functionf(x), if the limit of the…

Q: a. Find all functions from {0, 1} to {1}. b. Find two relations from {0, 1} to {1} that are not…

A: We have the domain is A=0,1 and the range is B=1 First we find the relations from A=0,1 to B=1: The…

Q: Refer to the following functions: p(x) = x2 + 2x – 15 x +1 9(x) x-3 r(x) = v7-x Which of the…

A:

Q: Let a, h, and k be arbitrary real numbers with a+0, and let f be the function given by the rule f(x)…

A:

Q: Which of the following families of real functions are algebras of functions? (For each, either show…

A: To check which of the given families are algebras of functions: Note that a function is said to be…

Q: D. Which of the following families of real functions are algebras of functions? (For each, either…

A:

Q: Let the function f be given by f(a) = 3a?. Which of the following is NOT a mathematically correct…

A: In the given question we have to choose a statement from the given statement which is mathematically…

Q: Let a, b, and c represent positive real numbers, where a 0. c. Solve f(x) < 0.

A: Answer(a):

Q: Which of the following families of real functions are algebras of functions? (For each, either show…

A: As per the question we are given three different families of functions from which we have to find…

Q: Let R denote, as usual, the set of all real numbers. Consider the following two functions: f: R→ R…

A:

Q: Let R denote, as usual, the set of all real numbers. Consider the following two functions: ƒ : R → R…

A: Given:The functions and  are given as: given by ; given by ., where  is the set of all real…

Q: (5) Given f(x) -2r and h(x)= simplify using the following operations: Write answers in standard…

A:

Q: 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.…

A: Domain or rational function of the form f(x)/g(x) is the set R- {x:g(x)=0}.

Q: Which of the following families of real functions are algebras of functions? (For each, either show…

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Q: D. Is the following familiy of real functions an algebras of functions? (either show it is an…

A: The answer provided below has been developed in a clear step by step manner.

Q: uv uw log- + log- + log– – log(uvw) W

A: Given,            loguvw+ loguwv+ logvwu -  loguvw

Q: . Which of the following families of real functions are algebras of functions? (For each, either…

A:

Q: Let X={1, 2, --, 16} and define function f(x)=r, for all rE X where r, is the remainder when 3* is…

A: Let X=1,2,...,16 and define function fx=rx for all x∈X, where rx is the remainder when 3x is divided…