Remember, the domain of a function refers to the value range of x, that is, the value range of the unknown.

The domain of f(2x- 1) is 0, 1, that is, 0≤x≤ 1, so-1≤ 2x-1≤

So the range of f(x) is 2x- 1, so the domain of f(x) is [- 1, 1].

If 1-3x is within the definition domain, F( 1-3x) is meaningful, that is,-1≤ 1-3x≤ 1 gives 0≤x≤2/3.

Will your problem solve itself?