4. (a) Let a : Z→ Z be the function defined by a(n) = 2n + 1, and let i: Z → Z be the identity function. Is there a function b: Z→ Z such that bo a = i? Is there a function b: Z → Z such that ao b = i? (b) Let f: N→ N and g: N→ N be defined by f(n) = n + 1, g(n) = Find the functions fog, gof, fogof and go fog. n 1 1 if n > 1 if n = 1.

Q: 5. Let f : R → [1, ∞) and g : [1, 0) → R be the functions defined by the following formulæ f (x) =…

A: Answer

Q: Let A = {1, 3, 4, 9, 10, 11} and B = {1, 4, 5, 6, 7, 10}. Consider the following function f: A B…

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Q: Let A = R - {1} and define f: A→A by f(x) = (a) Find fo f(x). (b) Find fofo f(x). (c) Find f-¹(x).…

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Q: 5. Consider the function f: Z15 → Z15 given by f([n]) = [n³]. Show that f is a function, and…

A: Given is a function f:ℤ15→ℤ15 by f([n])=[n3]   To Show: f is a function.   To Determine: Image of…

Q: 5. Let f : R -→ R be defined by f(x) = 2x +9. Find a formula for f-1.

A: We need to find the inverse function of the real valued function f(x)=2x+9

Q: Let f(r) = In r Find and simplify f"(x).

A: Please refer the attached image for complete solution. THANK YOU.

Q: 2. Let f: A → B and g: C → D be functions. The product of f and g is the function defined as…

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Q: 1. Give an example of a function f N N which is injective but not surjective.

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Q: 4. (a) Let f: X→Y, g: Y→ Z, and h: Y→ Z be functions. Prove or disprove: If gof=hof, then g = h. (b)…

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Q: 3. Determine whether each of these functions from is one-to-one/onto. (a) f : R → R, f(x) = 3r. (b)…

A: A function f is one-to-one if every element of the range of g corresponds to exactly one element of…

Q: 2. ( images. (a) f({0, 1, 2}) Let f: Z→ R, with f(n) = 4-n². Find the following direct and inverse…

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Q: 4. Let X an Y be sets with A, B C X and let f: X→Y be a function. Recall that {f(x) EYE A}, and…

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Q: F is a function from A to B. F is a function from P(A) --> P(B). If f is an injection prove F is an…

A: Given that f is a function from A to B that is f:A→B and F is function from PA to PB that is…

Q: 2. Let (r) be the function defined by V(x) = 1. Let 1+x. In(x) Vovo...(x) n-copies Note that…

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Q: 3. The function f(m, n) = 2"3" is a one-to-one function from N x N into N. (a) Calculate f(m, n) for…

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Q: 11. (a) Define f: RR by f(x) = x² - 4 for all x € R. Explain why the inverse of the function f is…

A: Step 1: Step 2:

Q: 3. Please help!!: Calculate the domain of the function

A: If you have any questions let me know in comment box thankyou for your question.

Q: 4. Determine whether each of the following functions is a bijection and if not bijection, 1 explain…

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Q: 7. Decide which of the following functions are (a) one-one, (b) onto, (c) both, (d) neither. (a) f :…

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Q: 1. Let A={1,3,5,7}. Let f:A→Z be the function f={(1,2),(3,4),(5,6),(7,8)}. Let g:Z→Z be defined by…

A: Given, Set A=1,3,5,7 and a two functions f and g as follows, f: A → Z by f=1,2,3,4,5,6,7,8 g: Z →Z…

Q: 11. (2.3.34) Let f: BC and g: A B be functions. (a) Prove or disprove the following statement: If…

A: let f:B→C and g:A→B be functions. (a) prove or disprove the following statement. if f∘g:A→C is an…