If f(x) = y = `(ax - b)/(cx - a)`, then prove that f(y) = x.

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

If y =(ax +b)/( cx + d) , then prove that 2y_1y_3=3(y_2)^2

y = f(x) = (ax-b)/(cx-a) then f(y) = ?

If y=f(x)=(a x-b)/(b x-a) , show that x=f(y)dot

If f(x)=log_(e)x, then prove that :f(xyz)=f(x)+f(y)+f(z)

If f(x)=cos(logx) , then prove that f((1)/(x)).f((1)/(y))-(1)/(2)[f((x)/(y))+f(xy)]=0

A function f : R rarr R satisfies the equation f(x+y) = f(x). f(y) for all x y in R, f(x) ne 0 . Suppose that the function is differentiable at x = 0 and f'(0) = 2 , then prove that f' = 2f(x) .

Let f(x)=((2008)^x+(2008)^(-x))/2,g(x)=((2008)^x-(2008)^(-x))/2 then prove that f(x+y)=f(x)f(y)+g(x)g(y)

If f(x+f(y))=f(x)+yAAx ,y in R and f(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dx .

If f(x)=(ax + b)sinx+(cx +d)cos x , then the values of a b, c and d such that f"(x)=xcos x for all x, then (a + b + c + d)is