Let z be the set of integers and f:Z → Z be defined as f(x)=-4x+5. Then the inverse function of f * does not exist because f is not one to one O None of these does not exist because f is not onto exists because f is bijective O O

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A: Please see the attachment

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Q: Let z be the set of integers and f:Z→Z be de fined as f(x) =-7x+2. Then the inverse function of f *…

A: Does not exists because f is not onto.

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A: First option is correct

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Q: Let Z be the set of integers and f:Z Z be defined as f(x)=-2x-3. Then the inverse function of exists…

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A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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Q: . Let f (x) = 11x +9x +21. Prove that f (x) is irreducible over Q.

A: We solve this problem using  (mod p ) irreducibility test over f(x) where p = 2 , a prime number.

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A: Equivalence Relation Definition : A relation R on a set A is said to be an equivalence relation if…

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Q: Let Z be the set of integers and f:Z -- Z be defined as f(x)=-2x-3. Then the inverse function of f *…

A: Let  f:ℤ→ℤ  given as fx=-2x-3.

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A: We have to check whether given statement is true or false.

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A: We  have to find out the solution

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A: For part a, principle of mathematical induction is used. For part b, function is defined when imagee…

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Q: 3. а) Prove by induction that 1 P(n):2+6+12+20+...+n(2n+2) = n(n+1)(n+2) Vn21 2 1 3 Let f:R→(-1,1)…

A: For a, principle of mathematical induction is used. For b, function is not well defined as images of…

Q: Let z be the set of integers and f:Z → Z be defined as f(x)=-4x+5. Then the inverse function of f *…

A: We know that inverse of a function exist if it is has one to one correspondence and it is onto. If…

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A: i have used the definition of onto functions and showed that c has no preimage under f  but gof is…

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A: Given that g:A→B is onto. If y∈B, then there exists a pre-image x∈A. ⇒g(x)=y

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A: Let F be a non trivial on X.To prove that the statements are equivalent:

Q: prove or disprove : If F:(R,+) (R\{0},.), defined by f(x)= x +2 is an isomorphism.

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A: Given: Two functions f : N → N and g : N → N are functions such that f is not onto but f + g is…

Q: Let F = {{n} : n ∈ Z} and G = {{r} : r ∈ R}. Find the smallest σ-algebra in Z containing F and the…

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