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f and g denote two motions. Is it true that f ◦ g is a translation...

f and g denote two motions.

Is it true that f ◦ g is a translation if and only if both f and g are translations? Justify your answer.

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Answer #1

False : If and   both are translation then is also an translation but if is an translation but    and   may not be an translation for example ,

is defined by .

   is defined by .

Then ,

So ,

That is is an translation but    and   is not an translation .

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