Why is that not considered 1 to 1 ? In a chapter of a calculus book before they get into limits, I can see that neither side of 1 has a limit from both directions. But the limit of f(x) from the left of x<1 , (1-x)=0 and the limit of f(x) from the right of x>=1 in sqrt(x-1)=0

Also since the union of the range of (1-x) and sqrt(x-1) is (-inf,1) U [1,inf) = (-inf,inf) every value of x is mapped to a single value of f(x) so whats the problem ? So why's that not considered 1:1 ? What am I forgetting or missing from pre-calculus math that says that's not 1:1