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1- find the pdt of real part of roots of z2-z= 5-5i is 2- find the natural no a for which summation of f(a+k)where k varies from 1 to n = 16 (2 to the power n-1) and fn f satisfies the relation f(x+y)= f(x)f(y) for all natural nos x,y and f(1)=2 i m unable to draw the graph of cot inverse (2x-x2), cot inverse of( x2-4x+3) and also find its domain and range 3- - fx= cos (lnx) then find( fx)(fy ) - o.5 ( f(x/y )+f(xy))

1- find the pdt of real part of roots of z2-z= 5-5i is
2-
find the natural no a for which summation of f(a+k)where k varies from 1 to n = 16 (2 to the power n-1) and fn f satisfies the relation f(x+y)= f(x)f(y) for all natural nos x,y and f(1)=2
i m unable to draw the graph of cot inverse (2x-x2), cot inverse of( x2-4x+3) and also find its domain and range
3-
- fx= cos (lnx) then find( fx)(fy ) - o.5 ( f(x/y )+f(xy))

Grade:12

1 Answers

Rinkoo Gupta
askIITians Faculty 80 Points
8 years ago
solution no.3
f(x)
cos(lnx)
so f(x)f(y)-1/2[f(x/y)+f(xy)]
=cos(lnx)cos(lny)-1/2{cos(ln(x/y))+cos(ln(xy))}
=1/2[2 cos(lnx)cos(lny)-{cos(ln(x/y))+cos(ln(xy))}]
=1/2[{cos(lnx+lny)+cos(lnx-lny)}-{cos(lnx/y))+cos(ln(xy))}]
=1/2[cos(ln(xy))+cos(ln(x/y))-cos(ln(x/y))-cos(ln(xy))]
=0

Thanks & Regards
Rinkoo Gupta
AskIITians Faculty

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