Suppose f : N→N and g :N→N , function f is not onto but f+g is onto function  does g onto function ?

Q: 5. Determine whether the function f : R+ → R defined by the rule f (x) = positive real numbers x in…

A: A function is said to be bijective if the function is both one one and onto. The given function is…

Q: Let f be a bounded function on [a,b] for which "f = ["f. Prove that f E R[a,b]. (Hint: Use the…

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Q: Define ƒ(1) in a way that extends ƒ(s) = (s3 - 1)/(s2 - 1) to be continuous at s = 1.

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Q: Let f : R → R be f(r) = + 1+ \|° (a) Is ƒ everywhere defined? If not, give the domaim (b) Is ƒ onto?…

A: Given, f: R→R be                       f(x)=x1+|x|

Q: Define f : Zmn → Zm × Zn by ƒ ([x]mn) = ([x]m, [x]n). Show that f is a function and that f is onto…

A: The function f:ℤmn→ℤm×ℤn is defined by                  fxmn=xm,xn Show f is a function and f is…

Q: For what codomain is f(x) an onto function? а. y4

A: Given: To identify that for what co-domain is function f(x) is onto function. Definition: Onto…

Q: Suppose that f’’ is continuous on [a,b] and that f has three zeroes in [a,b]. Show that f’’ has hat…

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Q: 2. Let a, b e R and let f be the function Z + Z defined by f(z) - ar + b. For which values of a and…

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Q: Exercise 9.23. Is there an analytic function f R→ R for which f(n) (0) = n for all n ≥ 0? If there…

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Q: Show that an onto function f :               {1, 2, 3} → {1, 2, 3} is always one-one.

A: Given, f :  {1, 2, 3} → {1, 2, 3}  is an onto function.

Q: Suppose that f is continuous on [0, 2] and that f(0) x, y in [0, 2] such that|y – x| = 1 and f(x) =…

A: If is given that f is continuous on 0, 2 and f0=f2. To prove: There exists x, y∈0, 2 such that y-x=1…

Q: Suppose that f is a function on [a, b] such that f(x) = 0 for all x e [a, b]\T , where T is finite…

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Q: Let A ϵ Mnxn(F). Under what conditions is det( - A) = det(A)?

A: To Determine: Let A ϵ Mnxn(F). Under what conditions is det( - A) = det(A)? Given: we have a matrix…

Q: 4. Let S = {x EN|3z ENA z? = x)). Let f : N → Sbe the function f(x) = x². Is f 1-1? Onto? Show why.

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Q: Prove that the function g: R > R defined by f(x) = 1+2^x is one-to-one but not onto.

A: Consider the function f:R->R defined by:

Q: Show that the functionf (x ,y)=xy³onD: x|<2, ]y|<oodoes not satisfies Lipschitz condition.

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Q: Give an example of onto but not 1-1 function f: 7⁰ → Z>⁰. tit 11-C.

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Q: Show that x is continuous everywhere. r(x)-x-0 XX<0

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Q: Let =[2,0}, then f is o- algebra.

A: Given a statement

Q: Let f :A→B and g : B +C be functions. Show that if g o f is onto, then g is onto.

A: Given: f:A→B and g:B→C are functions Given: gof: A→C is onto To show: g:B→C is onto That is,  for…

Q: Suppose that f is continuous on that 9< f(4) < 21. [0, 4], f(0) = 1, and 2 < f'(x) < 5 for all a in…

A: Here in this question we have a function which is both continuous and differentiable in the given…

Q: (a) f is a one-to-one function (Type Y for "yes" or N for "no") (b) ƒ is an onto function (Type Y…

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Q: A function from ZxZ to Z defined by f(m, n) = m-n is an onto function. O True O False

A: The given function is                                     f: ℤ×ℤ→ℤ  such that    f(m,n)=m-n. A…

Q: Let f be the function from {a, b, c, d} to {1, 2, 3} defined by f(a) = 3, f(b) = 2, f(c) = 1, and…

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Q: 2. If X is a finite set and fn → f on X, show that fn = f on X. 3. If fn 3 f on X and Y is a…

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Q: (b) If ƒ is continuous on (a, b) then there is a number c in (a, b) such that f(c) is an absolute…

A: Consider the statement  If f is continuous on (a,b) then there is a number c in  (a,b) such that…

Q: (5) Prove that Lp(f)<Uq(f) for any bounded function f and partitions P,Q of [a, b]. (Hint: Consider…

A: Note: According to Bartleby guidelines; for more than one question asked only the first one is to be…

Q: Let f(æ) = In(z') f'(2) =

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Q: A function from ZxZ to Z defined by f(m, n) = m-n is an onto function. True False

A: Here we will examine that f is onto or not.

Q: Give an explicit formula for a function from Z to Z+ that is a) onto, but not one-to-one. b)…

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Q: Let f be a continuous functio to R. Let a and b be two distinct ntained in U and fbe differentiable…

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Q: Suppose that fn ⇒ f on R and that each fn is a bounded function. Prove that f is bounded.

A: Solution

Q: if f is measurable then - f is messlurable

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Q: Let f(x) = vV72 – x and g(x) = x² – x. Give the domain of f o gusing interval notation.

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Q: (c) Suppose n = 5 and m = 4, determine the number of onto functions from A to B.

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Q: Let f: X→Y be a function. Please prove that if f(X-A)=Y-f(A) for any A⊆X, then f is onto.

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Q: 6. Is the function h: Z → Z defined by ( 2n if n 20 h(n) -n if n < 0 one-to-one? Is it onto?

A: The solution is given as follows

Q: 2. Let f: R → R_be f(x) = 1+ |r|" (a) Is f everywhere defined? If not, give the domain. (b) Is f…

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Q: Prove the following result: A function f that is decreasing on [a,b] is integrable on [a,b].

A: Prove the result that,        "A function f that is decreasing on[a,b] is integrable on[a,b]''

Q: Show that f (a) = is Libschitz function on r+ 2

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Q: Of f is a posittue differentiable furnction on. (00). (? (a+nx) ) Arone existo finitely .and…

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Q: Suppose f is a bounded real function on [a, b), and f' eR on [a, b). Does it follow that fe R? Does…

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Q: Let there be f: A--&gt;RShow that , if f is bounded in A , then f will also be bounded in B , where…

A: This can be proved as shown below.

Q: Let f:A at f is surjective. B and g: B -C be two functions. If gof is surjective and g is total…

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Q: 20. If f: X → Y and g: Y → Z are functions and gof is onto, must ƒ be onto? counterexample.

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Q: 20. Give two examples of functions from Z to Z that are one- to-one but not onto.

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Q: Determine whether the function f: Z x Z -→ Z is onto if f (m, n) = .m + n

A: We will solve the problem using the definition of onto function.

Q: 6. Show that if f(2) is continuous on a domain D, and if f(z)$ is analytic on D, then f(z) is…

A: Given :- If fz is continuous on a domain D. To Proof :- If fz8 is analytic on D , then fz is…

Q: Suppose functions w: PQ and h : Q+ R are both onto. Prove that the composite function is also onto.

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