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)) =

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A: Given table xf( x )-85-272962

Q: The function f: RR defined by f(x) = 5x3 + 3x2-x + 7 is O(x). True False

A:

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Q: Let f(z) then for all real number the power representation of f is Select one: O True O False

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Q: Consider f(x) = 99x2 − 100x + 101 and let x0,x1,x2,x3 be distinct. Without referring to the divided…

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A:

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Q: Determine F(x) if, for all real x and y, F(x)F(y) – F(xy) = x + y.   Hint:  What could F(1) be?

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A: From the given problem:   fx=x2+1 ; gx=x+2   So,   f+gx=fx+gx=x2+1+x+2=x2+x+3 Hence, f+g=x2+x+3.

Q: | Let f(x) = 2x³+3x²-x-5. Determine f[x0, x₁, x2, x3] and ƒ [x0, X₁, X2, X3, X4].

A: