Let f be a mapping from [1,+*[ to [1. +[ defined by f(x) = x+1/x. Then f has a unique fixed point O f(x)-f(y)Is2|x-yl and f has no fixed point. O if(x)-f(y)Is2|x-yl and f has a fixed point, O None of the choices.

Q: Give the domain of the function. z = 4x – 5y O {(x, y): x and y are real and 4x – 5y = 0} O {(x, y):…

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Q: Show that if f1(x) and f2(x) are functions from the set of positive integers to the set of real…

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Q: In(1 – x²) Vy – Vy? – 1 V1 - x2 (a) f(x, y) = (b) ƒ (x, y) = %3D

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Q: Do question 2 only

A: Given :-     A = { 1,2,3,4,5} and  relation R = { (4,1),(2,1),(3,2) } In the relation R, the domain…

Q: If a and b are integers, then a/b is always a rational number. True False

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Q: Do question 3 only

A: Step 1: Step 2: Step 3: Step 4:

Q: 3. Prove if the function f : R → R is defined by the rule f (x) = 4.x + 1 for all real numbers x,…

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Q: Do question 1 only

A: For any query with the solution, please ask in the comment box.

Q: (c) h: Z → Z. h(x) = x³ (d) f: Z - Z, f(x) E - 4 (e) f: Z- Z, f(x) = 5x - 4

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Q: Let f : R → R be defined as f(x) = x3 + 8 (i) Prove that f is a bijection (one-to-one…

A: Consider the given function.

Q: Determine the canonical form of the function f : R → R, f(x) = x2 − 4x + 6 and sketch its graph.

A: To determine the canonical form of f(x)=x2-4x+6 and to sketch its graph

Q: Let f(x) = (x + 1)² - 1, x 2-1. Then the set {x:f(x) = f(x)} is

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Q: Draw a function f that has the following characteris- tics, then write the zeroes of the function…

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Q: Determine whether the following relations R from A to B is a function or not. If the relation is not…

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Q: Draw a function f(z), defined for all real numbers z, with two local maximum and one local minimum.

A: We will draw a function which has two local maximum and one local minimum.

Q: Let A = {1,2,3}, B B = = Define the functions f: AC and g: B → C by f(1) = 7, f(2)= 9, f(3) = 7,…

A: We want g o h = f.     So, we want g o h(1) = f(1) = 7            and g o h(3) = f(3) = 7   Now,…

Q: Suppose a transformation has a mapping as follows:(x,y)→(1/2 x + 3, -2y + 4). If this mapping were…

A: Given: A function y=x and a transformation mapping x, y→12x+3, -2y+4.

Q: A: pp. A: px p. . A: pp(3)x3 + p(1)x.

A: “Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: Show that f(x) = e describes a bijective function from R to (0,+x). (a) Show that f is a function.…

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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: Find the domain and the range of the functions and describe it as regions in relevant spaces as well…

A: The objective is to evaluate the domain and range of x+116-x2-y22-z2. To find the domain and range…

Q: CONSIDER A FUNCTION OF R IN R DEFINED BY: x² + 1 X-2 SO, THE EXPRESSION: f(x) - f(3) x - 3 FOR 2 IS…

A: f is a function of R in R defined by  f(x)=( x2+1)/(x-2)  Then expression [ f(x)-f(3)]/(x-3) ?

Q: Find functions f and g from the set of positive integers to the set of real numbers such that f (n)…

A: Here, we need to find functions f and g from the set of positive integers to the set of real numbers…

Q: 4. Sketch the graph of the relation R= {(x, y)| x² – 2x – 2 < y < 2x – x² +

A: The given relation is,

Q: Suppose that a function ƒ(x) has the property that ƒ(x1 x2) = ƒ(x1) + ƒ(x2) for any two positive…

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Q: (1) Suppose that f and g are multiplicative functions. Prove that the function F defined by I…

A: Consider functions f and g to be multiplicative functions. To prove that function F defined by…

Q: A function f:R →→R, where R is the set of real- ax² + 5x - 8 numbers, is defined by f(x) = Find a +…

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Q: — 2х1 — 5х2 + 8хз x1+3x2 – 5x3 +x4 |3x1 + 11х2 — 19хз + 7x4 X +7x2 — 13хз + 5х4 x1 X2 . Let T X3 X4…

A: The given transformation T can be written as            Tx1x2x3x4=-2-58013-51311-19717-135x1x2x3x4is…

Q: D. Let function g: R → R be defined by g(x) = 2x + 1 5 cx in its domain. Why does your choice of c…

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