Let V be the set of functions f: RR. For any two functions f, g in V, define the sum f + g to be the function given by (f+g)(x) = f(x) + g(x) for all real numbers. For any real number c and any function f in V, define scalar multiplication cf by (cf)(x) = cf(x) for all real numbers. Answer the following questions as partial verification that V is a vector space. (Addition is commutative:) Let f and g be any vectors in V. Then f(x) + g(x)=for all real numbers since adding the real numbers f(x) and g(x) is a commutative operation. (A zero vector exists:) The zero vector in V is the function f given by f(x) = for all (Additive inverses exist:) The additive inverse of the function f in V is a function g that satisfies f(x) + g(x) = 0 for all real numbers. The additive inverse of f is the function g(x)=for all c. (Scalar multiplication distributes over vector addition:) If c is any real number and fand g are two vectors in V, then c(f+g)(x) = c(f(x) + g(x)) =

Q: Use the table to answer parts a) and b) about the function f(x). x f(x) -85 -2 7 29 6 2 a) Evaluate…

A: Given table xf( x )-85-272962

Q: 2. Find the domain for the following functions: x 4 3x a) b) c) √√x-7 x²+x-56 x²+4

A: As per Bartleby guidelines rule I am answering only three sub-part of a question. This question is…

Q: for all real nombers, as fllou) -7

A:

Q: - For the functions f(x) = x + 2 and g(x) = x - 3, which expression has the greatest value? a)…

A: We have given:Find the composite function :Find the composite function :

Q: Consider the following function: | 4x 9z -19 1 -1 -9z 19 f(2) = 3 13 0 0 0 a) What is the highest…

A:

Q: Suppose that the function h is defined, for all real numbers, as follows 1 3 h(x)= 2 x-5 if x #2 if…

A: Given function is h(x)=x23 if x≠22 if x=2We have to find the value of h(-2),h(2) and h(4)

Q: The function h is the reverse process of f. a. Fill in the following table to represent the…

A: NOTE: Refresh your page if you can't see any equations. . the function h subtracts 5 from each value…

Q: Given functions f and g, find fg. f(x) = 7x+2, g(x) = 4x + 5

A: we are given two functions and we need to find out the product of the functions.

Q: The maximum number of zeros for a quartic function is: 2 O 4 3 1

A: question is what is maximum number of zeros of a quartic function

Q: Find a → evaluation for the function (4n+1) 8¹ogn

A: Solution: f(n) = (4n + 1)8log n        = (4n + 1) (23)log n              [here , we assume base of…

Q: Indicate if the function is bijective from R to R, f (x) = −3x + 4, justify your answer

A: Given f : R→R, f(x)=-3x+4 Here the function is linear function. f'(x)=-3<0 for all x∈R Which…