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Question 999107: The binary operation * defined on the set of real numbers is a*b=a+b+5
A) show that the set of real numbers is closed with respect to *.
B) find the identity element.
C) given any element a, find its inverse.
Answer by josgarithmetic(39613)   (Show Source):
You can put this solution on YOUR website! (Removing the rendering tags because the rendering interferes with the specific notation used in the problem description);
(Parentheses also included in "inverse" section for the same reason):
a*b=a+b+5 basic model
Let e be an identity element to expect.
a*e=a+e+5=a
a+e+5=a
e=a-a-5
e=-5
On the other side,
e*a=e+a+5=a to expect,
e+a+5=a
e=a-a-5
e=-5
The identity element e, should be equal to -5.
Inverse:
Some number a^-1 should be the inverse.
a*a^-1=-5 must be expected.
a+a^-1+5=-5
a^-1=-5-5-a
a^-1=-(2)(5)-a-----the inverse.
Or if prefered,
a^-1=-((2)(5)+a)
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