I'm having trouble solving my homework and I would like some help.
S = [ -2 ; 2 ]. Check if the following sentence is true or false:
a) 2^(2x) - 2^x <= 0, for every X that belongs to S.
I can see that this is false because if I substitute X for 2 it is not <= 0, but i wanted to prove that the sentence was false.
What I did: 2^x = t.
t^2 - t <= 0 and found that the values i'm looking for are between 0 and 1
First root: 2^x <= 1
x <= 0
Second root: 2^x >= 0, so any value i can give to X will turn this sentence >= 0. And, of course, these values belong to S -> the sentence is true according to what I did, but my book says it is false.
Sorry for any mistake, english is not my native language and some notations might be wrong (I don't know if it is correct to call that a ''sentence'').