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If * is defined on the set Z of all int...

If * is defined on the set Z of all integers by *: a * b = `a+b-4`, find the inverse element, if exists in Z with respect to *

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The correct Answer is:
`atos;bto p;ctoq;d to r`
`atos,bto p,ctoq,d to r`
Let point F on the parabola be `(4t^(2),8t)`.
Tangent at this point is `ty=x+4t^(2)`
It meets the y-axis at (0,4t).
Then the area of triangle
EFG is `A(t)=2t^(2)(3-4t)=6t-8t^(3)`
Differentiating w.r.t, we get
`A'(t)=12t-24t^(2)`
For A'=0, t=1/2, which is a maxima. So, point F is (1,4).
slope of EF = 1
`:." "m=1orA(t)|_(max.)=(1)/(2)` sq. units
`y_(0)=4`
`andy_(1)=2`
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