If `f(x)=5^x` , then prove :
`f(x+y)=f(x).f(y)`

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

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

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

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

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

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

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 y= f(x)=(2x+3)/(5x-2) , prove that f(y)=x.

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