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 Post subject: are they equal?
PostPosted: Fri, 18 May 2012 13:53:06 UTC 
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True or false. The two functions f and g defined by

f(x) = 3x + 3 for x real and g(t) = 3t + 3 for t real and positive

are equal?

Thanks!


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 Post subject: Re: are they equal?
PostPosted: Fri, 18 May 2012 13:54:56 UTC 
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Radiologist wrote:
True or false. The two functions f and g defined by

f(x) = 3x + 3 for x real and g(t) = 3t + 3 for t real and positive

are equal?

Thanks!


What have you tried?

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\begin{aligned}
Spin(1)&=O(1)=\mathbb{Z}/2&\quad&\text{and}\\
Spin(2)&=U(1)=SO(2)&&\text{are obvious}\\
Spin(3)&=Sp(1)=SU(2)&&\text{by }q\mapsto(\mathop{\mathrm{Im}}\mathbb{H}\ni p\mapsto qp\bar{q})\\
Spin(4)&=Sp(1)\times Sp(1)&&\text{by }(q_1,q_2)\mapsto(\mathbb{H}\ni p\mapsto q_1p\bar{q_2})\\
Spin(5)&=Sp(2)&&\text{by }\mathbb{HP}^1\cong S^4_{round}\hookrightarrow\mathbb{R}^5\\
Spin(6)&=SU(4)&&\text{by the irrep }\Lambda_+\mathbb{C}^4
\end{aligned}


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 Post subject: Re: are they equal?
PostPosted: Fri, 18 May 2012 15:50:23 UTC 
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Radiologist wrote:
True or false. The two functions f and g defined by

f(x) = 3x + 3 for x real and g(t) = 3t + 3 for t real and positive

are equal?

Thanks!

if you draw the graph you will get a good idea that range of f and g are not same.more over g>3 where as f can take all real value.

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 Post subject: Re: are they equal?
PostPosted: Fri, 18 May 2012 21:37:28 UTC 
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Radiologist wrote:
True or false. The two functions f and g defined by

f(x) = 3x + 3 for x real and g(t) = 3t + 3 for t real and positive

are equal?

Thanks!


No, it says explicitly that their domains are not the same, so they are not the same function.

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