If `x lt y` and `b<0,` then `(x)/(b)>(y)/(b).` Prove It.

(i) If y = f(x) = (3x-1)/(5x-3) , prove that f(y) = x (ii) If y = f(x) = (ax -b)/(bx-a) , prove that f(y) = x

If the point P(x, y) is equidistant from the points A(a + b, b - a) and B(a - b, a + b). Prove that bx = ay.

If (x)/(l)+(y)/(m)=1 is any line passing through the intersection point of the lines (x)/(a)+(y)/(b)=1 and (x)/(b)+(y)/(a)=1 then prove that (1)/(l)+(1)/(m)=(1)/(a)+(1)/(b)

If y=f(x)=(ax-b)/(bx-a) , the prove that : x=f(y)

If y^(2)=xz and a^(x)=b^(y)=c^(z), then prove that (log)_(a)b=(log)_(b)c

if a,b,c are in G.P. and a^(x)=b^(y)=c^(z) prove that (1)/(x)+(1)/(z)=(2)/(y)

If a^(x)=b,b^(y)=c and c^(z)=a, prove that xyz=1

If the point (x,y) is equidistant from the points (a-b,a+b) and (-a-b,a+b) . Prove that x+b=0