Find all the strictly monotonic functions f: R→R such that f(x + f(y)) = f(x) + y, for all z, y € R. Prove that for every integer n > 1 there do not exist strictly monotonic functions f: R-R such that f(x+ f(y)) = f(x) +y”, for all z, y ER.

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A: The given function is: f(x)=1-4x2   0≤x&lt;1x2-2x1≤x&lt;2

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A: Let's find.

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A: The answer to this question is given below.Explanation:

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A: By choosing x=y=0. Also by choosing x=y we can see f(2x)=4f(x).  Moreover choose x=0 and use f(0)=0,…

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A: We shall use the intermediate value theorem to answer this question

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A: all the values which can be used as input in a function is called domain of a function

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Q: 3. Let f(x) = { ,x<2 ax + b, x22 Find a and b so that f (2) exists.

A: To find the value of a and b

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