If is an inner-product function , then : Select one: a. equals one b. equals zero c. is greater than or equal zero d. is greater than one

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Q: Define functions H and K from R to R by the fol- lowing formulas: For every x ER, H(x) = (x– 2)² and…

A: Observe the given functions as follows.

Q: Find a codomain B such that ƒ: A → B, ƒ(x) = e²´ is surjective. Show that g: B → A, g(x) = Vln x is…

A: As you asked only subpart (C) and (D) So, I answered here only subpart (C) and (D).

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A: Let us define a bijective functions. We know that , a function f : X → Y is bijective if it is both…

Q: Consider the following function. f (x) = In (1 + 2x), a = 5, n = 3, 4.6 < x < 5.4

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Q: For an arbitrary function f: XY, prove the following identities: a) f¹ (Uiel Bi) = Uier f-¹ (B₁). b)…

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Q: Iff is not Lipschitz function de fined on [a, b] then f ¢ R [a, b] True O False O

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Q: Consider the following functions from R to R. For each of them, determine whether it is one-to-one,…

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Q: Use the IVT to show that if f is continuous and one-to-one on an interval [a, b], then f is either…

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Q: In the given question, explain why Rolle’s Theorem does not apply to the function even though there…

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Q: ctions, determine its domain, codomain, and range.    f: Z × Z → Z, f(m, n) = 3m

A: Introduction: The Domain refers to what can be put into a function. The Codomain is what may or may…

Q: Let g : B → C and h : B → C be functions. Suppose that go f = hof for every function f: A → B. Prove…

A: We have to prove that g(x) = h(x) for all x belongs to B.

Q: Find and classify the discontinuities of the following function as removable or nonremovable. If a…

A: Consider the function    ux=x2-9x-5 Removable discontinuity:-   A discontinuity at a point x=a  is…

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A: Given: ft=t+2t2-4. first we have to simplify given function then check for continuity ft=t+2t2-22…

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Q: Let f(x) = V12 – æ and g(x) = æ² – x. - What will be the domain of the composite function, fog ? The…

A: Let A,B and C be two non-empty sets, a function f:A→B and g:B→c, the composition of f and g is…

Q: : Let f [a, b] → R be a continuous and one-to-one function, where a < b are real numbers. Use the…

A: Introduction: There must be at least one "c" such that c∈(a,b) (or a&lt;c&lt;b) and f(c) = L. if…

Q: Explain if the function is continuous or not for the given number a. if x > 1 f(x) = {1 if x = 1…

A: topic - limits and continuity

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: Determine b so that f(x) is continuous if O 8 x + 6 xS 6 f( x ) = D O 2 x2 + bx +10 x > 6 b =

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Q: Let f: X →Y be an injective function, and A, B C X. Prove that Q1) f(A)n f(B) C f(AN B).

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Q: Define H(x) as a piecewise defined function and evaluate H(1), H(2), H(3), H(0) and H(-2) given by,…

A: We have to solve the problem by just putting the value in the piecewise function.

Q: Suppose that f : A → B and g : B → C are both injective functions, prove that the function go f : A…

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Q: Suppose that a continuous function g satisfies: | g(x)dr = 24 and 9(2x)da = 21. 0. .2 Find

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Q: Is the function f(x) = x + 1 from the set of integers to the set of integers onto?

A: For onto from set A to B, Every value of set B should exist atleast once in the function.

Q: Let f(x) = -. Does f(-2+h) equal or -2 +h :-2 with h = 0.5. Compute the difference quotient at a = +

A: Given: fx=1x

Q: Show that the GHASH function calculates (X1 • H™) Ð (X, · H"-1) © O (Xm-1° H²) O (Xm· H) ...

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Q: Define a function S : Z+ → Z+  as follows. For each positive integer n, S(n) = the sum of the…

A: Define a function S : Z+ → Z+  as follows. For each positive integer n, S(n) = the sum of the…

Q: Suppose that f:R → R is a continuous odd function, such that 1 f(x) dx = 5 and -1 | f(x) f(x) dx =…

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Q: Is the cobb-douglas function strictly concave when a1 +a2 <1 when

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Q: Let f(x) = { if x - 4 m= mx 6 - If f(x) is a function which is continuous everywhere, then we must…

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Q: 3) Show that f = f, ху for the following function: ху (x° у) f(x. y) + In(x° + y30 ) 20

A: We have to prove that fxy = fyx

Q: Suppose that f : A → B is a function, C C A and DC B. (a) If f is surjective, prove that D = =…

A: Given- Suppose that f : A → B is a function, C ⊆ A and D ⊆ B.  To Prove- If f is surjective, prove…

Q: Let f : A → B be a function. Prove that f is surjective if and only if, for every pair of functions…

A: Please comment if you need any clarification. IF you find my answer useful put thumbs up. Thank you.

Q: b. f(x) = xe-*, g(x) =; -1<x< 5. Show in a single space. 2x

A: Given that, fx=xe-x, gx=12x; -1≤x≤5 Plot the following functions over the defined domain.

Q: Let f : A → B be a function. Prove that if C C A and D C A and f is injective, then f(C) = 7 (D) =→…

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Q: Let f : S → T be a function, and let A and B be subsets of T. Prove or give a counterexample to the…

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Q: If the function f(x) is even, which of the following is ze an O bn ao nothing is zero

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Q: g(x) = x²mx, -2, mx+b, if x 1.

A: We can solve this as follows:

Q: sketch the given function and determine whether it is piecewise continuous on[0,∞).

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Q: Determine if the function is continuous on the given interval. - 1. f(x) = √x² – 25 ; [−6, −5] 2.…

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Q: Define a function S : Z+ → Z+ as follows. For each positive integer n, let S(n) = the sum of the…

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Q: a. f(x) x-2 x-7 b.f(x) = r2+1

A: (a) the given function is f(x)=1x-2 the function is continuous in interval [a,b] if it is continuous…

Q: Show that the following functions are continuous: (a) f (x) = k (k any constant)          (b) g(x) =…

A: (a) Given:          fx=k k any constant Let c be any real number f is continuous at x = c if…

Q: Please prove the following statement

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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: A function f :N Z which is one-to-one and onto.

A: Suppose we have a function . Condition of f is one-one . Suppose such that , then . Condition…

Q: Find the libraries toon L(x) of the functions at a.

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Q: Express the following functions in the form u+iv f (z) = In(z)

A: The complex number: z=x+iy can be written as z=reiθ, where r=x2+y2 and θ=tan-1yx. Using the…