If `f(x)=y=(alphax-b)/(c x-a), AA x in R -{a/c} & a^(2) ne bc` then prove that f(y)=x

f((x)/(y))=f(x)-f(y)AA x,y in R^(+) and f(1)=1, then show that f(x)=In x

f(x+f(y))=f(x)+y AA x,y in R and f(0)=1f(x+f(y))=f(x)+y AA x,y in R and f(0)=1 then prove that int_(0)^(2)f(2-x)dx=2int_(0)^(1)f(x)dx

Let f be a one-one function such that f(x).f(y) + 2 = f(x) + f(y) + f(xy), AA x, y in R - {0} and f(0) = 1, f'(1) = 2 . Prove that 3(int f(x) dx) - x(f(x) + 2) is constant.

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

If f is polynomial function satisfying 2+f(x)f(y)=f(x)+f(y)+f(xy)AA x,y in R and if f(2)=5, then find the value of f(f(2))

Let f(x+y)+f(x-y)=2f(x)f(y)AA x,y in R and f(0)=k, then

If f(x) is a quadratic expression such that f(x)gt 0 AA x in R , and if g(x)=f(x)+f'(x)+f''(x) , then prove that g(x)gt 0 AA x in R .

Let f(x)=x^(2)+ax+b. If AA x in R, there exist a real value of y such that f(y)=f(x)+y, then find themaximum value of 100a.