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a fixed point of a function f is a number c in its domain such that...

a fixed point of a function f is a number c in its domain such that f(c)=c. use the intermediate value theorem to prove that any continious function with domain [0,1] and range a subset of [0,1] must have a fixed point.[hint: consider the function f(x)-x]
“Recall the intermediate value theorem:suppose that f is countinous function with domain[a,b]and let N be any number between f(a)and f(b), where f(a)not equal to f(b). Then there exist at least one number c in [a,b] such that f(c)=N

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