Concept guide
Domain, codomain and range: a finite table and the range of h(x)=x²+1
(1) With A={−1,0,1,2}, B={0,1,2,3,4,5} and f(x)=x²+1: verify that f:A→B is a total function, find the range f[A], and show f[A]⊆B but f[A]≠B; (2) explain why data with an output outside the declared codomain, or with a missing input, is not a total function in the sense of this entry; (3) for h:ℝ→ℝ, h(x)=x²+1, prove that the range is [1,∞), which differs from the codomain ℝ.