Show that the function f: Real #s to Real #s defined by f(x)=x2 is not a homomorphism.

Q: = Let f: R\(2)→ R\[5] be a function defined by f(x): Show that f is bijective. 5x+1 x-2

A: Bijection function: if f is bijective function then the function f is must be  1)one-one function…

Q: Show that the function f (x) = 1- x is bijective and also find (i) its inverse function.

A: Bijective Function :  A function is said to be bijective or bijection, if a function f: A → B…

Q: Let f(x) = x2 / (x2-1) . (a) From a graph of f, explain why f is not invertible. Furthermore,…

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Q: Let the function f: R→ R be defined by f(x) = { Question 1 0, x2, x=0, x = 0. (a) Explain the…

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Q: Prove that the function given by f(x) =x3-3x2+3x-100 is increasing in R

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Q: 2. Prove that a) the function f(x) = tan x+x can be replaced by g(x) =x if x→0. b) the function…

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Q: 14. Show that if f is a monotone function defined on [a, b] that satisfies the intermediate value…

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Q: Suppose that f and g are functions, and that they are left inverses of each other. Prove that f og…

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Q: Suppose that f is differentiable on some open interval containing c, and (c,f(c)) is a point of…

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Q: Give examples of two functions             f : N → Z and g : Z → Z such that g o f is injective but…

A: First of all, consider the definition for the injective function.Injective function is one-to-one…

Q: 2. Consider the following four functions from R into R, determine if onto or 1-1 function. Support…

A: To find out which of the following function is one-one,  onto .

Q: Define g(-5) in a way that extends g(x)= 9(-5) = x² - 25 x + 8x + 15 to be continuous at x = -5.

A: We have to define g(-5) such that g(x) is continuous at x = -5.

Q: If f and g are both odd functions, is their product necessarily odd, even or neither? Prove it

A: Given data: *f and g are both odd function. By the definition of the odd function if a function f(x)…

Q: Let F be the collection of all functions f: N-→ {0,1}. Is F countable ?

A: A set S  is countable if there exists a one-to-one map from the set to the set of all-natural…

Q: (a) Assume that f(x) is a function defined by f(x) = x²-3x+1 2x - 1 for 2 ≤ x ≤ 3. Prove that f(x)…

A: Given.

Q: Suppose that ƒ : [a, b] → R is a continuous and one-to-one function. Prove that ƒ is strictly…

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Q: Suppose that f : [a,b] → R is a continuous and one-to-one function. Prove that f is strictly…

A: We will prove this by contradiction.

Q: Define functions f: A B nd g: B C. Prove that if / and g are both injective, then their composite…

A: Let the function f:A→B and g:B→C is defined as, fa=b and gb=c. To prove the functions f and g are…

Q: Let f(x) = { 3, 1< x < 2 0, 2 < a <5 and Let F(x) = { 3x, 1<x < 2 6, 2 <x < 5 Show that wether the…

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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: Suppose f and g are functions with domain R. If both f and g are even but f+g is odd, then prove…

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Q: Show whether or not f is bijective. Then, give the range of f. a. Let f: ZN be defined as f(x)=…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Let f(x)= 1 Use a 8- e proof to show that f is continuous at x = = 2. X-1

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Q: Suppose that f :C → C is integer and that ƒof = f. What can you say about f ? Justify your answer.…

A: Please find the answer in next step

Q: Consider the following functions. (c) f: GL₂(R) → RX, f + ((ad)) (($)) (d) f: GL₂(R) → R, ƒ (e) f:…

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Q: Assume that f(x) is a function defined by f(x) x²-3x+1 2x1 for 2 ≤ x ≤ 3. Prove that f(x) is bounded…

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Q: Use the limit definition of a derivate to compute f'(x) for the given function. 18. f(x) = x² + 2x +…

A: In this question we have to find the derivative of f(x) using the limit definition.

Q: 6. Prove that there does not exist a multiplicative function f such that f(30) = 0, f(105) = 1, and…

A: We have to prove the given statement.

Q: Let f be a function from R - {1} to R given by f(x) = x/(x-1). Then f is surjective; injective;…

A: Given function is f(x) = xx-1

Q: Determine whether the function f : R\{2} –>R\{0}, defined by f(x)=(1/(x-2)) is bijective or not.

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Q: Letf(x)= 1/x-1 Use a 8-e proof to show that f is continuous at x = 2.

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Q: Define g(3) in a way that extends g(x) = (x? - 9)/(x - 3) to be continuous at x = 3. %3D

A: Given, g(x)=x2-9x-3

Q: form the graph of f(x) into th 5) f(x) = x³ g(x) = -(x – 2)° %3D 3 %3D

A: We have to find

Q: Define g(4) in a way that extends g(x) = (x2 - 16)/(x2 - 3x - 4) to be continuous at x = 4.

A: On simplification, we get

Q: Define h as x 2 Determine whether the function h is continuous h(x) = {3, x2 or discontinuous at x…

A: NOTE: Refresh your page if you can't see any equations. . if the function h(x) is continuous at x=2…

Q: Determine whether the function f (x) = {: —х in — 1 <x<0 in 0<x < 1 is even or odd,

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Q: Is the function f(x) = x2 from the set of integers to the set of integers onto?

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Q: ) Let f: A-B be a function which is not surjective and g : B C which is bijective. Prove that g of:…

A: See full proof below

Q: Let n be a positive integer and let f: [0..n] - (0..n] be an injective function. Define the function…

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Q: Let Z4 denote the set of positive integers and consider the function f : Z+ → Z, defined by f(n) =…

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Q: Suppose f is a function which satisfies the properties: f(x + y) = f(x) + f(y) + x²y + ry? %3D for…

A: It is given that fx+y=fx+fy+x2y+xy2 for all real numbers x and y. Substitute y=0 in…

Q: Let f and g be the function from the set of integers to itself, defined by f(x) = 2x + 1 and g(x) =…

A: Consider the two given functions. fx=2x+1 gx=3x+4   The composition of the functions f and g  is…

Q: Show that if f is symmetric with respect to x = a, then g(x) = f (x + a) is even.

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Q: Prove that f is an identity function of itself.

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Q: Let f: {4,5,6} → {1,2,3} be a function defined by f(x) = x-3. Prove that f is injective and…

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Q: Define g(3) in a way that extends g(x) = (x2 - 9)/(x - 3) to be continuous at x = 3.

A: Here, the given function The function gx is continuous at  x=a, if the following holds: (i) ga is…