Let f be a continuous, g be a discontinuous function. Prove that `f + g` is discontinuous function.

f+g may be a continuous function, if (a) f is continuous and g is discontinuous

The function f(x) =cot x is discontinuous on set

The function f(x) =cot x is discontinuous on set

The function f(x)=tanx is discontinuous on the set

Statement 1: f(x)=cos x is continous at x=0a n dg(x)=[tanx],"w h e r e"[dot] represents greatest integer function, is discontinuous at x=0,t h e nh(x)=f(x)dotg(x) is discontinuous at x=0. Statement 2: If f(x) is continous and g(x) is discontinuous at x=a ,t h e nh(x)=f(x)g(x) is discontinuous at x=a

Which of the following statements is always true? ([.] represents the greatest integer function. a) If f(x) is discontinuous then |f(x)| is discontinuous b) If f(x) is discontinuous then f(|x|) is discontinuous c) f(x)=[g(x)] is discontinous when g(x) is an integer d) none of these

The function f(x)=(4-x^2)/(4x-x^3) a)discontinuous at only one point b) discontinuous exactly at two points c)discontinuous exactly at three points d) none of these

The function f(x)=(4-x^2)/(4x-x^3) (a) discontinuous at only one point (b) discontinuous exactly at two points (c) discontinuous exactly at three points (d) none of these

The functions g(x)=x-[x] is discontinuous at x =

f is a continous function in [a, b] ; g is a continuous function in [b,c]. A function h(x) is defined as h(x)=f(x) for x in [a,b) , g(x) for x in (b,c] if f(b) =g(b) then