`" A function "f:R rarr R" satisfies the equation "f(x)f(y)-f(xy)=x+y" and "f(y)>0" ,then "f(x)f^(-1)(x)=`

A function f:R rarr R satisfies the equation f(x)f(y)-f(xy)=x+y AA x,y in R and f(1)>0, then f(x)f^(-1)(x)=x^(2)-4bf(x)f^(-1)(x)=x^(2)-6c*f(x)f^(-1)(x)=x^(2)-1d none of these

A function f:R rarr R satisfy the equation f(x)f(y)-f(xy)=x+y for all x,y in R and f(y)>0, then

" Let "f:R rarr R" satisfy relation "f(x)f(y)-f(xy)=x+y AA x,y in R" and "f(1)>0" .If "h(x)=f(x)f^(-1)(x)" ,then length of longest interval in which "h(sin x+cos x)" is strictly decreasing is."

A function f:R rarr R" satisfies the equation f(x+y)=f(x)f(y) for all values of x" and "y and for any x in R,f(x)!=0 . Suppose the function is differentiable at x=0" and "f'(0)=2 , then for all x in R,f(x)=

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

A function f:R rarr R satisfies the differential equation 2xy+(1+x^(2))y'=1 where f(0)=0 then

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) .

A function f:R rarr R satisfy the equation f(x).f(y)=f(x+y) for all x,y in R and f(x)!=0 for any x in R. Let the function be differentiable at x=0 and f'(0)=2, Then : Then :

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

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) .