If `f:Rto[0,oo]` be a function satistying the property `f(x+y)-f(x-y)=f(x)[f(y)-f(-y)] `for all ` y, xepsilonR`, `f^(')(0)=ln a, f(0)=1`
`f(x)` is

If f:Rto[0,oo] be a function satistying the property f(x+y)-f(x-y)=f(x)[f(y)-f(-y)]Aay, xepsilonR, f^(')(0)=In a, f(0)=1 The soluton of differential equation (dy)/(dx)=((log_(a)f(x)+log_(a)f(y))^(2))/([log_(a)f(x)+2][log_(a)f(y)-2]) is

If the function / satisfies the relation f(x+y)+f(x-y)=2f(x),f(y)AAx , y in R and f(0)!=0 , then

If f(x+y)=f(x)f(y) for all real x and y, f(6)=3 and f'(0)=10 , then f'(6) is

If f((x)/(y))=(f(x))/(f(y)) for all x,y in R,y!=0 and f(t)!=0, if t!=0 and f'(1)=3 then f(x) is

If f(x+y)=f(x) xx f(y) for all x,y in R and f(5)=2, f'(0)=3, then f'(5)=

If f(x+y)=f(x). f(y) for all x and y and f(5)=2, f'(0)=4, then f '(5) will be