Question

Xét tính chẵn lẻ

a, y=\(\left|2x+1\right|+\left|2x-1\right|\)

b, y=2x^{2 +} \(\left|x\right|\)

^{c,y= \(\dfrac{\left|x+1\right|+\left|x-1\right|}{\left|x+1\right|-\left|x-1\right|}\)}

Cảm ơn nha.

Answer 1

a) đặc \(f\left(x\right)=y=\left|2x+1\right|+\left|2x-1\right|\)

\(D=R\) \(\Rightarrow\forall x\in D\) thì \(-x\in D\)

ta có : \(f\left(-x\right)=\left|-2x+1\right|+\left|-2x-1\right|=\left|2x-1\right|+\left|2x+1\right|=f\left(x\right)\)

\(\Rightarrow\) hàm này là hàm chẳn

b) đặc \(f\left(x\right)=y=\dfrac{\left|x+1\right|+\left|x-1\right|}{\left|x+1\right|-\left|x-1\right|}\)

\(D=R\backslash\left\{0\right\}\) \(\Rightarrow\forall x\in D\) thì \(-x\in D\)

ta có : \(f\left(-x\right)=\dfrac{\left|-x+1\right|+\left|-x-1\right|}{\left|-x+1\right|-\left|-x-1\right|}=\dfrac{\left|x-1\right|+\left|x+1\right|}{\left|x-1\right|-\left|x+1\right|}\)

\(=-\dfrac{\left|x+1\right|+\left|x-1\right|}{\left|x+1\right|-\left|x-1\right|}=-f\left(x\right)\)

\(\Rightarrow\) hàm này là hàm lẽ