Umkehrfunktionen Aufgaben

a)

$y=\frac{1}{2}(x-2{)}^2+1$	$D_f=\mathbb{R}$
$\overline{y}=\sqrt[3]{2(\overline{x}-1)}+2$	$W_f=\mathbb{R}$

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f(x)=1/2*(x-2)^2+1
g(x)=pow(2*(x-1),3)+2

b)

$y=3(x+2{)}^5-6$	$D_f=\mathbb{R}$
$\overline{y}=\sqrt[5]{\frac{\overline{x}+6}{3}}-2$	$W_f=\mathbb{R}$

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f(x)=3*(x+2)^5-6
g(x)=pow((x+6)/3,1/5)-2

c)

$y=\frac{1}{4(x+2)}$	$D_f=\mathbb{R}\text{textbackslash}\{-2\}$
$\overline{y}=\frac{1}{4x}-2$	$W_f=\mathbb{R}\text{textbackslash}\{0\}$

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f(x)=1/(4*(x+2))
g(x)=1/(4*x)-2

d)

$y=\frac{3}{(x-1{)}^3}$	$D_f=\mathbb{R}\text{textbackslash}\{1\}$
$\overline{y}=\sqrt[3]{\frac{3}{\overline{x}-2}}+1$	$W_f=\mathbb{R}\text{textbackslash}\{2\}$

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f(x)=3/((x-1)^3)
g(x)=pow(3/(x-2),1/3)+1

e)

$y=2(e^{\frac{x}{4}-4}-4{)}^3-1$	$D_f=\mathbb{R}$
$\overline{y}=3(\ln (\sqrt[3]{\frac{\overline{x}+1}{2}+4})+4)$	$W_f=\text{textbraceleft}x\in \mathbb{R}\text{textbrokenbar}x>-129\text{textbraceright}$

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f(x)=2*(E^(x/4)-4)-4
g(x)=(ln(x+0.5)-3)/2

i)

$y=e^{2x+3}$	$D_f=\mathbb{R}\text{textbackslash}\{1\}$
$\overline{y}=\frac{\ln \overline{x}+\frac{1}{2}-3}{2}$	$W_f=\mathbb{R}\text{textbackslash}\{2\}$

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f(x)=E^(2x+3)
g(x)=(ln(x+0.5)-3)/2