2. Let f : R → R be a continuous function. Suppose that (f o f) (x) = x for every x E R. (a) Prove that there exists a point c ER such that f (c) Hint: Consider the function g (x) = f (x) – x for...

2. Let f : R → R be a continuous function. Suppose that (f o f) (x) = x for<br>every x E R.<br>(a) Prove that there exists a point c ER such that f (c)<br>Hint: Consider the function g (x) = f (x) – x for every x € R.<br>= C.<br>(b) Give an example for a function satisfying the above requirements,<br>and such that f id, -id , where id is the identity function.<br>

Extracted text: 2. Let f : R → R be a continuous function. Suppose that (f o f) (x) = x for every x E R. (a) Prove that there exists a point c ER such that f (c) Hint: Consider the function g (x) = f (x) – x for every x € R. = C. (b) Give an example for a function satisfying the above requirements, and such that f id, -id , where id is the identity function.

Jun 03, 2022

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2. Let f : R → R be a continuous function. Suppose that (f o f) (x) = x for every x E R. (a) Prove that there exists a point c ER such that f (c) Hint: Consider the function g (x) = f (x) – x for...

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