Statement-1: If `f(x + y) = f(x) + f(y),` then fis either differentiable everywhere or not differentiable everywhere.Statement-2: Any function is either differentiable everywhere or not differentiable everywhere

If f(x)=max{sinx ,sin^(-1)(cosx)}, then f is differentiable everywhere f is always continuous f is discontinuous at x=(npi)/2,n in I f is not differentiable everywhere

The function f(x)=e^(-|x|) is continuous everywhere but not differentiable at x=0 continuous and differentiable everywhere not continuous at x=0 none of these

The function f(x)=e^(-|x|) is continuous everywhere but not differentiable at x=0 continuous and differentiable everywhere not continuous at x=0 none of these

If f(x)=max{sin x,sin^(-1)(cos x)}, then f is differentiable everywhere f is always continuous f is discontinuous at x=(n pi)/(2),n in If is not differentiable everywhere

Let f(x)={2x+3 for x 1 if f(x) is everywhere differentiable, prove that f(2)=-4

If f(x) is differentiable everywhere, then which one of the following is correct?

If f(x) is differentiable everywhere, then which one of the following is correct?

Let f(x)=|cosx| (a) Then, f(x) is everywhere differentiable (b) f(x) is everywhere continuous but not differentiable at x=npi,\ \ n in Z (c) f(x) is everywhere continuous but not differentiable at x=(2n+1)\ pi/2,\ \ n in Z (d) none of these

If f(x+y)=f(x)dotf(y),\ AAx in R\ a n df(x) is a differentiability function everywhere. Find f(x) .