Odpowiedź:
1)
[tex]a)\\|2-\sqrt{5} |=-(2-\sqrt{5} )=\sqrt{5} -2\\b)\\2\sqrt{3} -|3-2\sqrt{3} |=2\sqrt{3} +(3-2\sqrt{3} )=2\sqrt{3} +3-2\sqrt{3} =3\\c)\\|-2,6|-|-3,3|=2,6-3,3=-0,7[/tex]
2)
a)
f(x)=x-|x|
[tex]f(x)=\left\{\begin{array}{ccc}2x&\mbox{dla}&x < 0\\0&\mbox{dla}&x\geq 0\\\end{array}\right[/tex]
b)
f(x)=2|x+3|
[tex]f(x)=\left\{\begin{array}{ccc}-2x-6&\mbox{dla}&x < -3\\2x+6&\mbox{dla}&x\geq -3\\\end{array}\right[/tex]
c)
f(x)=x*|x|
[tex]f(x)=\left\{\begin{array}{ccc}-x^{2} &\mbox{dla}&x < 0\\x^{2} &\mbox{dla}&x\geq 0\\\end{array}\right[/tex]
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Odpowiedź:
1)
[tex]a)\\|2-\sqrt{5} |=-(2-\sqrt{5} )=\sqrt{5} -2\\b)\\2\sqrt{3} -|3-2\sqrt{3} |=2\sqrt{3} +(3-2\sqrt{3} )=2\sqrt{3} +3-2\sqrt{3} =3\\c)\\|-2,6|-|-3,3|=2,6-3,3=-0,7[/tex]
2)
a)
f(x)=x-|x|
[tex]f(x)=\left\{\begin{array}{ccc}2x&\mbox{dla}&x < 0\\0&\mbox{dla}&x\geq 0\\\end{array}\right[/tex]
b)
f(x)=2|x+3|
[tex]f(x)=\left\{\begin{array}{ccc}-2x-6&\mbox{dla}&x < -3\\2x+6&\mbox{dla}&x\geq -3\\\end{array}\right[/tex]
c)
f(x)=x*|x|
[tex]f(x)=\left\{\begin{array}{ccc}-x^{2} &\mbox{dla}&x < 0\\x^{2} &\mbox{dla}&x\geq 0\\\end{array}\right[/tex]