Let f : R → R be defined as                   f(x) = x4 Choose the correct answer.(A) f is one-one onto                              (B) f is many-one onto(C) f is one-one but not onto.                (D) f is neither one-one nor onto.

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A:

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A:

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

A:

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Q: Let f(2) := 25. Show that f is invertible in a neighbourhood of i and calculate (f-1Y(/(i)).

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Q: T is a function?

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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.

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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: Prove that f : R → R by f(x) = 2x+4. Prove that f is one-to-one and maps surjectively onto R.

A:

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: Let f map C2 into C2 be a linear operator such that for every x in C2, f(f(x)) = x. Let V+ = {x in…

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Q: (a) Prove that there exists a function f: Z → Z so that f is one-to-one but f is not onto. (b) Prove…

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Q: 8. If f is conformal on a domain D which is symmetric with respect to the real axis, is f(z)…

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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.

A:

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Q: Determine whether or not the function f : Z × (Z − {0}) → Z is onto, if f((m, n)) = ⌊m/n ⌋

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Q: (a) Prove that there exists a function f : Z→ Z so that f is one-to-one but f is not onto. (b) Prove…

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Q: 1. If f:X → Y and g:Y → Z are functions and gof is onto. a. Must g be onto? Give a proof or a…

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Q: 3 10. Prove the function f : R- {1}- R-{1} defined by f(x) = ()° is bijective. %3D |

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A: A function f: A→B is said to be one-one if        f(x1)=f(x2)   ∀x1, x2∈A         ⇒x1=x2 In words,…