# Math Help - a question about function?

1. ## a question about function?

Please show me some continuous function with a domain in the closed interval [0,1] and its range is also [0,1].

2. The identity map

$f:[0,1]\to [0,1]$
$f(x)=x$

is a continuous function with domain and range $[0,1]$

3. 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 $n\in \mathbb{Z}^+$, a positive integer.
Then $f(x)=x^n$ will work.

4. thank u so much. it seems very simple.