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Let Q be the set of all rational numbers...

Let Q be the set of all rational numbers and let `**` be a binary operation on `QxxQ` defined by `(a,b)**(c,d)=(ac,b+ad).`
Determine whether `**` is commutative and associative. Find the identity element for `**` and invertible elements of `QxxQ.`
Or Let `f:[0,oo) toR` be a function defined by `f(x) =9x^(2)+6x-5.` Prove that f is not invertible. modify only the condomin of f to make f invertible and then find its inverse.

Text Solution

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The correct Answer is:
`**` is not commutative, `**` is associative, (1,0) is the indentity, inverse of (a,b) is `((1)/(a),(-b)/(a))`
Or, `f^(-1)(y)=(sqrt(y+6)-1)/(3)`
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