Question

Va rog ,ajutati-ma!!

Answer 1

a)
x<0 deci |x|=-x
-x<0<2deci |2-x|=|x-2|=-x+2
atunci
-x+3x+2-x+2=x+4


b) x<6 deci |x-6|=6-x=-x+6
x>0 deci √x^4=|x²|=x², pt ca x²≥0, deci x>0 este dat degeaba

x²+2≥2>0 deci |x²+2|=x²+2
atunci

x²+2-x²-x+6+6x-2=6x-x+6=5x+6



c)
x>-4 deci x+4>0 deci |x+4|=x+4

x<2 deci x-2<0 deci√(x-2)²= |x-2|=-x+2
si |2x-6|=2|x-3| dar x<2<3 deci decix-3<0, deci  |x-3|=-x+3
atunci
x+4-x+2-2(-x+3)=6+2x-6= 2x

Answer 2

a)

[tex]\it E(x) = |x| +3x+2+|2-x| \\ \\ x \ \textless \ 0 \Rightarrow |x| =-x \\ \\ x\ \textless \ 0 \Rightarrow -x \ \textgreater \ 0|_{+2} \Rightarrow 2-x\ \textgreater \ 0 \Rightarrow |2-x| = 2-x[/tex]

Expresia devine:

$\it E(x) = -x+3x+2+2-x = x +4$

b)

 [tex]\it x^2+2\ \textgreater \ 0 \Rightarrow |x^2+2| = x^2+2; \ \ \ \sqrt{x^4} = x^2 \\ \\ x\ \textless \ 6\Rightarrow x-6\ \textless \ 0 \Rightarrow |x-6| = 6-x \\ \\ E(x) = x^2+2-x^2+6-x+6x-2 = 5x +6[/tex]

c)

[tex]\it x\ \textgreater \ -4 \Rightarrow x+4\ \textgreater \ 0 \Rightarrow |x+4| =x+4 \\ \\ \sqrt{(x-2)^2} = |x-2|,\ \ \ x\ \textless \ 2 \Rightarrow x-2\ \textless \ 0 \Rightarrow |x-2| = 2+x \\ \\ x\ \textless \ 2|_{\cdot2} \Rightarrow 2x\ \textless \ 4\ \textless \ 6 \Rightarrow 2x\ \textless \ 6\Rightarrow 2x-6\ \textless \ 0\Rightarrow \\ \\ \Rightarrow |2x-6| = 6-2x[/tex]

$\it E(x) = x+4+2-x -(6-2x) = 6 - 6+2x =2x$