- Grow STEM Panel
- “Working in STEM Outside Academia”
- Wed. Nov. 30, 5:00 PM
- Newton 204
- Section 6.6
- Suppose h(x) = x3, A = [-1,1], B = [0,2]. How does h(A∩B) relate to h(A) ∩ h(B)?
- If f : A → B and S ⊆ A, then f(S) = { f(a) | a ∈ S }
- h : R → R
- h(A) = [-1,1]
- h(B) = [0,8]
- h(A∩B) = [0,1] = h(A) ∩ h(B)
- Theorem: h(A∩B) ⊆ h(A) ∩ h(B)
- What if S∩T = ∅? f(∅) = ∅
- What about g(x) = x3 - 3x with same A and B?
- A = [-1,1], B = [0,2]
- A = [-1,1], B = [0,2]
- Can you make (and prove) any conjectures about when f(A∩B) = f(A) ∩ f(B) vs when
f(A∩B) ⊂ f(A) ∩ f(B)?
- Conjecture: f has to be a bijection?
- Conjecture: maybe being an injection is enough (per book’s exercise 14)
- Relations
- Read section 7.1