Consider the function g : Z × Z → Z defined g(x, y) = |x| − |y|, prove if it is onto or not? Is it one-to-one or not?

Q: Let f : R → R be a function with the following property: |f (a) – f(b)| < 4|a – b| for all a, b E R.

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Q: Find a 1-1 function f from J onto S where Sis the set of all odd integers.

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Q: Let R={(x,y) ERxR: |x| = |v|). Then R a function on R. оо True False

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Q: 5. Prove that the function f: Z → Z defined by f(x) = 3x + 1 is one-to-one.

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Q: Let f : R → R be a function defined by f(x) = Decide whether it is an injection, a surjection, 1+ x2…

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Q: Show that the set of functions 1,cosx,sinx,cos2x,sin2x,…,cosmx,sinmx,… is orthogonal on the interval…

A: We are given the following functions: 1, cosx, sinx, cos2x, sin2x,…, cosmx, sinmx, …   Our aim is to…

Q: Let f : R → R be a function given by f(x) = 2x – 1 (a) Determine whether f is bijective or not. (b)…

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Q: Show that the function Arg(z) is not continuous on each point of the non-positive real axis.

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Q: Show that the mapping f:R2 → R² defined by f(x1, x2) 5x2) is linear. = (2x1 + x2, -3x1 +

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Q: f: R → R f(x) = -5x Select the correct description of the function f. O Neither one-to-one nor onto…

A: Given function is f: ℝ → ℝf(x) = -5x

Q: Let S = {0,1}. Exhibit all functions S → S and classify them as injective, surjective, bijective, or…

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Q: Is the set X of all functions f: Z+→ {0, 1} countable? Prove or disprove.

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Q: Let ƒ : R¹00 → R be the function that sends each point (x1, x2, X3,. the sum of its coordinates.…

A: The function  such that it maps  to the sum of its coordinates.The aim is to find the value of the…