Give an example of an increasing function whose domain is the interval [0,1]but whose range does not equal the interval[f(0),f(1)]

Question

please show me the work

Answer 1

well, f(x) = 1/(1-x)

has range = [1,oo) but it's sort of a bad candidate because f(1) is not defined, so [f(0),f(1)] does not exist.

Gotta think more on this one.