Suppose that f: [a, b][a,b] is continuous. Prove that there is at least one fixed point in[a, b] - that is, x such that f(x)=x.
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Originally Posted by lacy1104 Suppose that f: [a, b][a,b] is continuous. Prove that there is at least one fixed point in[a, b] - that is, x such that f(x)=x. Hint: Define $\displaystyle g(x) = f(x) - x$. Now use intermediate value theorem to show $\displaystyle g$ has a zero on $\displaystyle [a,b]$.
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