Let `f(x+y)=f(x)+f(y)` for all `xa n dydot` If the function `f(x)` is continuous at `x=0,` show that `f(x)` is continuous for all `xdot`

If f((x+y)/3)=(2+f(x)+f(y))/3 for all x,y f'(2)=2 then find f(x)

A function f(x) satisfies the following property: f(xdoty)=f(x)f(y)dot Show that the function f(x) is continuous for all values of x if it is continuous at x=1.

A function f(x) satisfies the following property: f(x+y)=f(x)f(y)dot Show that the function is continuous for all values of x if its is continuous at x=1.

f(x+y)=f(x).f(y) for all x,yinR and f(5)=2,f'(0)=3 then f'(5) is equal to

Is the function defined by f(x)= |x| , a continuous function?

Let f be a function such that f(x+y)=f(x)+f(y) for all xa n dya n df(x)=(2x^2+3x)g(x) for all x , where g(x) is continuous and g(0)=3. Then find f^(prime)(x)dot

Let f(x+y)=f(x)dotf(y) for all xa n dydot Suppose f(5)=2a n df^(prime)(0)=3. Find f^(prime)(5)dot

If for a function f : R to R f (x +y ) =F(x ) + f(y) for all x and y then f(0) is

Show that the function defined by f(x)= |cos x| is a continuous function.

Let f(x)={(log(1+x)^(1+x)-x)/(x^2)}dot Then find the value of f(0) so that the function f is continuous at x=0.