Please show me some continuous function with a domain in the closed interval [0,1] and its range is also [0,1].
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The identity map $\displaystyle f:[0,1]\to [0,1]$ $\displaystyle f(x)=x$ is a continuous function with domain and range $\displaystyle [0,1]$
Originally Posted by boxxkutexx Please show me some continuous function with a domain in the closed interval [0,1] and its range is also [0,1]. Suppose that $\displaystyle n\in \mathbb{Z}^+$, a positive integer. Then $\displaystyle f(x)=x^n$ will work.
thank u so much. it seems very simple.
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