Hi, this is my first time here so tell me if I do anything wrong. I am in L1 in science and I have an assignment in analysis but I have severe executive dysfunction and I can't get on with my work even though I know it's not very difficult. I also never know if what I do is enough and I get stuck when I actually have to write what I think. Basically I can't do anything.
This is a quickly translated version of an exercise of that assignment, I only did the question 1 and 2-1.
Q1 :
f(A) = {y ∈ F | ∃ x ∈ A y=f(x)} or {f(x) ∈ F | x ∈ A} ∈ P(F) *I think I'll use the first one.
f^-1(B) = {x ∈ E | f(x) ∈ B}
Q2 :
1. f(0) = 2[0/2] = 2[0]
f(1) = 2[1/2] = 2[0]
f(3/2) = 2[(3/2)/2] = 2[0]
f(2) = 2[2/2] = 2[1]
f(3) = 2[3/2] = 2[1]
f(4) = 2[4/2] = 2[2]
f(5) = 2[5/2] = 2[2]
I know that, in the Q3, in order to show that f(^-1(f(E)) = E I have to prove that f^-1 is bijective, but again, nothing want to come out of my brain.
Thank you to anyone willing to help me.
This is a quickly translated version of an exercise of that assignment, I only did the question 1 and 2-1.
Q1 :
f(A) = {y ∈ F | ∃ x ∈ A y=f(x)} or {f(x) ∈ F | x ∈ A} ∈ P(F) *I think I'll use the first one.
f^-1(B) = {x ∈ E | f(x) ∈ B}
Q2 :
1. f(0) = 2[0/2] = 2[0]
f(1) = 2[1/2] = 2[0]
f(3/2) = 2[(3/2)/2] = 2[0]
f(2) = 2[2/2] = 2[1]
f(3) = 2[3/2] = 2[1]
f(4) = 2[4/2] = 2[2]
f(5) = 2[5/2] = 2[2]
I know that, in the Q3, in order to show that f(^-1(f(E)) = E I have to prove that f^-1 is bijective, but again, nothing want to come out of my brain.
Thank you to anyone willing to help me.