Exercise · ZW-SURJECTIVE-FUNCTION-006 · ★☆☆ Basic
What is the name of the set \(f(A)\) of all values taken by \(f\)?
Choose one option.
Show answer
- D. The image of \(f\)
Explanation
The image \(f(A)=\{f(a):a\in A\}\) collects the values reached. It equals \(B\) exactly when \(f\) is surjective. The domain is \(A\), and the codomain is \(B\).
Review the concept: Surjective function
Function \(f\colon A\to B\) whose image is the whole codomain \(B\).
\[\forall b\in B\,\exists a\in A\,(f(a)=b)\]
More practice problems: surjective function
- ZW-SURJECTIVE-FUNCTION-001 What does it mean for fcolon A→ B to be surjective?
- ZW-SURJECTIVE-FUNCTION-002 Which of these functions from ℝ to ℝ is surjective?
- ZW-SURJECTIVE-FUNCTION-003 What is the logical form of the definition of a surjective function?
- ZW-SURJECTIVE-FUNCTION-004 If fcolon A→ B is not surjective, what holds?
- ZW-SURJECTIVE-FUNCTION-005 Let fcolon\1,2,3\→\a,b\. Can f be surjective?
- ZW-SURJECTIVE-FUNCTION-007 Let fcolonℤ→ℤ, f(n)=2n. What is the image f(ℤ)?
- ZW-SURJECTIVE-FUNCTION-008 Let A=\1,2,3,4\ and B=\a,b\. How many surjective functions fcolon A→ B are there?
- ZW-SURJECTIVE-FUNCTION-009 If fcolon A→ B and gcolon B→ C are surjective, is g∘ f?