3. Construct a bijection f: [0, 1] → (0, 1) UN.

Q: Q13) A series is: Q.14) A sequence (()) a) converge by comparison test c) converge by integral test…

A: Here are the two solutions given below. Please go through .

Q: (6) Define T1,T2,T3 : R³ → R³ by T1 T3( y ) Y y – z (a) Find TT2( y). (b) Suppose that T1,T2, T|T2…

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Q: 18. Determine whether each of these functions is a bijec- tion from R to R. a) f(x) = -3x + 4 b)…

A: As per guidelines, we will solve first three subparts of the question. a) Given function is fx=-3x+4…

Q: Q: Show that the functi on f:R →R given by f (x) = ax +b, where ab e R, a #0 is a bijection.

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Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: 2. For F = (xz3, 2y*x²,5z?y) find: a. div F b. Curl F and find div(curl F) C.

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Q: Let f:R → R such that f(x) = x² – 2x + 1. Verify whether f is bijective ? explain your answer.

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Q: Suppose that the translation T is described by (?,?)→(?+2,?−1)(x,y)→(x+2,y−1). What translation…

A: We have to find the translation described in x,y→x+2,y-1.

Q: 9. Find bijective functions from R to R a) f (x) = 2x + 1 b) f(x) = x² + 1 c) f (x) = x³ %3D x2+1 d)…

A: As per our guideline we are allowed to do 1 question or maximum 3 subparts at a time. Please post…

Q: 1. Define f : (- o, 2) → (- 0, 1) by f(x) = . Show that f is bijective. x+1 *-2

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Q: 3. Let f(x, y) = (2x – y,x- 2y); (x, y) E R x R, (R is set of real numbers.) a) Show that f is one…

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Q: IS a function.. (b) Let R= {(x,y) € R × R : 1 < ¤ < 4 or x = 6}, %3D and S = {(x, y) E R × R : –1 <…

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Q: Show that f: R\{2} → R\{5} defined by f(x) = (5x+1)/(x - 2) is bijective.

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Q: Construct the truch table for (pq) (rs)

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Q: Consider f: Z+ → Z defined as follows. x)=2x-1 Isf a bijection (YES NO and JUSTIFY)? 2. Consider f:…

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Q: Show that the mapping f:R2 → R² defined by f(x1, x2) 5x2) is linear. = (2x1 + x2, -3x1 +

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Q: Show that  ℝ2 = span([1 1], [1 -1])

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Q: a) Give an example of an algebraic function f : Z → Z that is injective but not surjective. You do…

A: Since this is a multiple question according to the Bartleby Answering rule, only first question is…

Q: b) Find 4°f(x) if f(x) = (3x+1)(3x+4)(3x+7) ... (3x + 19) %3D

A: We will answer the first question only as we don't answer multiple question at a time. Please…

Q: 2) Let R= {(1,2), (3,4), (1,x)) in order to this relation NOT be a function x must be equal ? a) 1…

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Q: If z = 1 - 2j and w= 2 - 3j, express 2. w in the form a + bj where a and b are real.

A: Given  z=1−2jw=2−3j

Q: 3x +1 III.(10) Prove that the function f: R – {5} –> R – {3} defined by f(x) = is a bijection. x- 5

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Q: f: X → Y and g: Y→ V be bijective functions. Show the following: ) gof: X → V is injective. gof: X→V…

A: It is given that f:X→Y and g:Y→V are bijective functions.

Q: Find ß so that {1, x, 1+ 6x²) on (-1,1) is orthogonal.

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Q: For the function f given by f(2) = 32 + 3 evaluate f(z + h) - f(x) a) 06h + 3z b) 0-6h + 3z c) 06h +…

A: Given  f(x)=3x2+3So,f(x+h)=3(x+h)2+3

Q: Show that f : R → R is bijective, where: f(x) %3D필

A: A function is injective if f(x)=f(y)⇒x=y. A function is onto if for every y in Y there exists a x in…

Q: Derive/prove following relations: a) (A x B) (C × D) = A· [B x (C x D)] = A• [(B. D)C - (B. C)D] (A.…

A: We know that the dot product of resultant of two cross product is called scalar quadruple product.…

Q: Find if the following is homothetic: F (x,y) = x²y +y3 %3D 1. Yes, it is homothetic. 2. No, it is…

A: topic -  homogenous funtion

Q: be the vector spaces consisting of zero and polynomials in z of degree <3 and degree < 6…

A: Given that  and  are two vector spaces consisting of  and polynomials of degree  and degree…

Q: Find a bijection between the interval (−1, 1) and R.

A: