# Concept derivation guides

299 concept teaching guides, separate from the 36,000 individual question derivations.

[Search all questions & derivations →](/en/explore/)

1 1 results · Page 1 of 1



Concept guide



## [Domain, codomain and range: a finite table and the range of h(x)=x²+1](/en/derivations/derivation-mko-domain-codomain-range-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-domain-codomain-range)

(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.

Domain, codomain, and range

derivation-mko-domain-codomain-range-01





1 1 results · Page 1 of 1