Câu 1:
\(f\left(-x\right)=\left(-x\right)^4-3\cdot\left(-x\right)^2+1\)
\(=x^4-3x^2+1=f\left(x\right)\)
Vậy: f(x) là hàm số chẵn
\(c1:D=R\Rightarrow\forall x\in D\Rightarrow-x\in D\)
\(\Rightarrow f\left(-x\right)=x^4-3x^2+1=f\left(x\right)\Rightarrow hàm\) \(số\) \(chẵn\)
\(c2:cm:\overrightarrow{AC}+\overrightarrow{BD}=2\overrightarrow{MN}\)
\(M,N\) \(trung\) \(điểm\) \(AB,CD\Rightarrow\left\{{}\begin{matrix}\overrightarrow{MA}+\overrightarrow{MB}=\overrightarrow{0}\\\overrightarrow{DN}+\overrightarrow{CN}=\overrightarrow{0}\end{matrix}\right.\)
\(\overrightarrow{MN}=\overrightarrow{MB}+\overrightarrow{BC}+\overrightarrow{CN}\)
\(\overrightarrow{MN}=\overrightarrow{MA}+\overrightarrow{AD}+\overrightarrow{DN}\)
\(\Rightarrow2\overrightarrow{MN}=\overrightarrow{MB}+\overrightarrow{MA}+\overrightarrow{BC}+\overrightarrow{AD}+\overrightarrow{CN}+\overrightarrow{DN}\)
\(=\overrightarrow{0}+\overrightarrow{BC}+\overrightarrow{AD}+\overrightarrow{0}\Rightarrow2\overrightarrow{MN}=\overrightarrow{AD}+\overrightarrow{BC}\left(đpcm\right)\)
\(c3:D=R\text{[}-5;\text{+∞.)}\)
\(f\left(x\right)\) \(nghịch\) \(biến\Leftrightarrow a< 0\)
\(\Rightarrow-5\le a< 0\left(a\in Z\right)\Rightarrow a=\left\{-5;-4;-3;-2;-1\right\}\)
\(c4:\) có công thức \(X\cap Y=X+Y-X\cup Y=25+20-36=9\)
Làm dưới dạng tự luận ( giúp mình với ạ :< )
