If the square ABCD, where `A(0,0),B(2,0)C(2,2) and D(0,2)` undergoes the following three transformations successively
(i) `f_(1)(x,y) to (y,x)`
(ii) `f_(2)(x,y) to (x+3y,y)`
(iii) `f_(3) (x,y) to ((x-y)/2,(x+y)/2)`
then the final figure is a

A rectangle ABCD, where A-=(0,0),B-=(4,0),C-=(4,2)D-=(0,2) undergoes the following transformations successively: f_(1)(x,y)rarr(y,x)f_(2)(x,y)rarr(x+3y,y)f_(3)(x,y)rarr((x-y)/2),(x+y)/2) The final f_(3)(x,y)rarr((x-y)/2),(x+y)/2 ) The final figure will be square (b) a rhombus a rectangle (d) a parallelogram

Determine whether the following represents a circle , a point or no circle : (i) 1- x^(2) - y^(2) = 0 (ii) x^(2) + y^(2) + 2x + 1 = 0 (iii) x^(2) + y^(2) - 3x + 3y + 10 = 0 .

Let f(x+y) + f(x-y) = 2f(x)f(y) for x, y in R and f(0) != 0 . Then f(x) must be

If f(x+y) = f(x) + f(y) + |x|y+xy^(2),AA x, y in R and f'(0) = 0 , then

Find the point of intersection of the straight lines : (i) 2x+3y-6=0 , 3x-2y-6=0 (ii) x=0 , 2x-y+3=0 (iii) (x)/(3)-(y)/(4)=0 , (x)/(2)+(y)/(3)=1

If f((x+2y)/3)=(f(x)+2f(y))/3\ AA\ x ,\ y in R and f^(prime)(0)=1 , f(0)=2 , then find f(x) .

If f((x+2y)/(3))=(f(x)+2f(y))/(3)AA x,y in R and f'(0)=1,f(0)=2 then find f(x) .