Homework Soursea Find a continuous function f01 R with an image equal to R
a. Find a continuous function f:(0,1) --> R with an image equal to R.
b. Find a continuous function f:(0,1) --> R with an image equal to [0,1].
c. Find a continuous function f:R --> R that is strictly increasing and has an image equal to (-1,1
b. Find a continuous function f:(0,1) --> R with an image equal to [0,1].
c. Find a continuous function f:R --> R that is strictly increasing and has an image equal to (-1,1
Solution
a) tan((x-1/2))
b) [sin(2x)]2
c) arctan(x)*2/
(it has positive derivative 2/*1/(1+x2) so it is strictly increasing and since the range of arctan is (-/2,/2) we obtain what we want)
![a. Find a continuous function f:(0,1) --> R with an image equal to R. b. Find a continuous function f:(0,1) --> R with an image equal to [0,1]. c. Find a](/WebImages/25/a-find-a-continuous-function-f01-r-with-an-image-equal-to-r-1064150-1761556359-0.webp "a. Find a continuous function f:(0,1) --> R with an image equal to R. b. Find a continuous function f:(0,1) --> R with an image equal to [0,1]. c. Find a")
