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Hello everyone,
How can I prove that the following function is surjective?
f(a, b) = a/b for (a, b) in ZxZ*
Many thanks.
Hello!
I'm trying to prove that the following function is bijective and find its inverse function.
Let X be a set and A a subset of X.
f : P(X) → P(X)
A → the complement of set A
It's the first time I'm asked to do this with power sets and sets, so I have no idea of what I'm supposed to do.
All help is much appreciated!
Thanks so much!
Hello,
How can I prove that the following function is surjective?
f : N → Z such that :
f(x) = x/2 if x is even
f(x) = -(x+1)/2 if x is odd
Many thanks!
Understood. Thank you so much!
Hello!
I'm struggling with the following question :
True or false?
If f,g : R → R are defined as f(x) = |x−1| et g(x) = |x+1| then the composite function g ◦ f verifies, for x ∈ R :
(g ◦ f)(x) = 2-x if x ≤ 1,
(g ◦ f)(x) = x if x > 1,
I'm pretty sure that (g ◦ f)= |x-1|+1. However, I don't know how to continue. I've graphed all three functions and the statement seems true to me, but I'm not very confident.
Can someone confirm if the statement is true or false? If it's true, how can I prove it? If it's false, how can I disprove it?
Thanks in advance!
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