`"I f"f(x)={x^3-6x^2; ifxi sr a t ion a l-11 x+6;ifxi si r r a t ion a l"t h e n"` `f(x)` is continuous for all real `x` `f(x)` is continuous at `x=1,2,3.` `f(x)` is discontinuous at infinite points `f(x)` discontinuous for all real `xdot`

Find the value of x where f(x)={x ,ifxi sr a t ion a l1-x ,ifxi si r r a t ion a li scon t inuou sdot

Statement-1: If |f(x)| le |x| for all x in R then |f(x)| is continuous at 0. Statement-2: If f(x) is continuous then |f(x)| is also continuous.

If f(x)={x ,xi sr a t ion a l1-x ,xi si r r a t ion a l ,t h e nf(f(x)) is xAAx in R (b) {x , xi si r r a t ion a l1-x ,xi sr a t ion a l {x ,xi sr a t ion a l1-x ,xi si r r a t ion a l (d) none of these

Leg f(x+y)=f(x)+f(y)fora l lx , y in R , If f(x) is continue at x=0,s howt h a tf(x) is continuous at all xdot

If f(x) = sec 2x + cosec 2x, then f(x) is discontinuous at all points in

Statement I f(x) = sin x + [x] is discontinuous at x = 0. Statement II If g(x) is continuous and f(x) is discontinuous, then g(x) + f(x) will necessarily be discontinuous at x = a.

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

Leg f(x+y)=f(x)+f(y)fora l lx , y in R , If f(x)i scon t inuou sa tx=0,s howt h a tf(x) is continuous at all xdot

If f (x) has isolated point of discontinuity at x=a such that |f (x) | is continuous at x=a then :

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