User:Bekesidaniel/Aufgabe 64

a)

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  <math> y=x^{-3} \qquad \qquad \qquad D=\mathbb{R}\setminus \left \lbrace0\right \rbrace
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  <math> y=x^{-2} \qquad \qquad \qquad D=\mathbb{R}\setminus \left \lbrace0\right \rbrace
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  <math> y=x^{-1} \qquad \qquad \qquad D=\mathbb{R}\setminus \left \lbrace0\right \rbrace
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  $y=x^{0}\qquad \qquad \qquad D=\mathbb {R}$
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  $y=x^{1}\qquad \qquad \qquad D=\mathbb {R}$
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  $y=x^{2}\qquad \qquad \qquad D=\mathbb {R}$
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  $y=x^{3}\qquad \qquad \qquad D=\mathbb {R}$

--Bekesidaniel (talk) 21:25, 8 January 2010 (UTC)--87.97.90.223 (talk) 21:23, 8 January 2010 (UTC)

c)

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  ${\sqrt {x}}=x^{1/2}\qquad \qquad \qquad D=\mathbb {R} _{+}\ \cup \ \left\lbrace 0\right\rbrace$
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  ${\sqrt[{3}]{x}}=x^{1/3}\qquad \qquad \qquad D=\mathbb {R} _{+}\ \cup \ \left\lbrace 0\right\rbrace$
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  ${\sqrt[{3}]{x^{2}}}=x^{2/3}\qquad \qquad \qquad D=\mathbb {R} _{+}\ \cup \ \left\lbrace 0\right\rbrace$

--Bekesidaniel (talk) 21:25, 8 January 2010 (UTC)--87.97.90.223 (talk) 21:23, 8 January 2010 (UTC)

e)

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  $y=(3x-2)^{2}+1\qquad \qquad \qquad D=\mathbb {R}$

---Bekesidaniel (talk) 21:25, 8 January 2010 (UTC)-87.97.90.223 (talk) 21:23, 8 January 2010 (UTC)

f)

Siehe a)

$1/{x^{-3}}=x^{3}$

$1/{x^{-2}}=x^{2}$

$1/{x^{-1}}=x^{1}$

$1/{x^{0}}=x^{0}$

$1/{x^{1}}=x^{-1}$

$1/{x^{2}}=x^{-2}$

$1/{x^{3}}=x^{-3}$

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  $y=1/{\sqrt {x}}\qquad \qquad \qquad D=\mathbb {R} _{+}\setminus \left\lbrace 0\right\rbrace$

--Bekesidaniel (talk) 21:25, 8 January 2010 (UTC)--87.97.90.223 (talk) 21:23, 8 January 2010 (UTC)

g)

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  $y=exp(x)=e^{x}\qquad \qquad \qquad D=\mathbb {R}$
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  $y=exp(-x)\qquad \qquad \qquad D=\mathbb {R}$
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  $y=exp(2x)\qquad \qquad \qquad D=\mathbb {R}$
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  $y=exp(x/3)\qquad \qquad \qquad D=\mathbb {R}$
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  $y=exp(1-x)\qquad \qquad \qquad D=\mathbb {R}$
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  $y=exp(x-1)\qquad \qquad \qquad D=\mathbb {R}$

--Bekesidaniel (talk) 21:25, 8 January 2010 (UTC)--87.97.90.223 (talk) 21:23, 8 January 2010 (UTC)

h)

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  $y=ln(x)\qquad \qquad \qquad D=\mathbb {R} _{+}\setminus \left\lbrace 0\right\rbrace$
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  $y=ln(2x)\qquad \qquad \qquad D=\mathbb {R} _{+}\setminus \left\lbrace 0\right\rbrace$
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  $y=log_{10}(x)\qquad \qquad \qquad D=\mathbb {R} _{+}\setminus \left\lbrace 0\right\rbrace$
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  $y=ln(2x-1)\qquad \qquad \qquad D=\mathbb {R} _{\setminus }\left\lbrace 0\right\rbrace$
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  $y=log_{2}(2x-1)\qquad \qquad \qquad D=\mathbb {R} _{+}\setminus \left\lbrace 0\right\rbrace$

--Bekesidaniel (talk) 21:25, 8 January 2010 (UTC)--87.97.90.223 (talk) 21:23, 8 January 2010 (UTC)

i)

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  $y=sin(x)\qquad \qquad \qquad D=\mathbb {R}$
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  $y=cos(x)\qquad \qquad \qquad D=\mathbb {R}$
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  $y=sin(\Pi *x)\qquad \qquad \qquad D=\mathbb {R}$
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  $y=sin(x+\Pi /2)\qquad \qquad \qquad D=\mathbb {R}$

--Bekesidaniel (talk) 21:25, 8 January 2010 (UTC)--87.97.90.223 (talk) 21:23, 8 January 2010 (UTC)