[" 4कि "y=f(x)=(x+2)/(x-1)," तो सिद्ध कीजिए कि "],[x=f(y)" ."]

If y=f(x)=(2x-1)/(x-2), then f(y)=

If y=f(x) =(x+2)/(x-1)(x ne 1,-2) then show that x=f(y)

A: If y = x ^(y) then (dy)/(dx) = (y ^(2))/(x(1- log y )) If y = f (x) ^(y), then (dy)/(dx) = (y ^(2) f '(x))/(f (x) [1- ylog f (x)])= (y ^(2) f'(x))/(f (x) [1- log y])

If f(x) = (x-1)/(x+1) , then prove that (f(x)-f(y))/(1+f(x)f(y))=(x-y)/(1+xy) .

If f(x+y)=f(x)+f(y) for all real x and y, show that f(x)=xf(1) .

Let f(x) be a function such that f(x).f(y)=f(x+y) , f(0)=1 , f(1)=4 . If 2g(x)=f(x).(1-g(x))

If f(x) is a real valued and differentaible function on R and f(x+y)=(f(x)+f(y))/(1-f(x)f(y)) , then show that f'(x)=f'(0)[1+t^(2)(x)].