Show that `f(x)={1+x^2, if 0<=x<=1, 2-x,\ \ \ if\ x >1` is discontinuous at `x=1` .

Let f(x)=(1-cosx)/(x^2),\ \ \ w h e n\ x!=0,\ f(x)=1,\ \ \ w h e n\ x=0 . Show that f(x) is discontinuous at x=0 .

Let f(x)={(1-cosx)/(x^2),\ \ \ w h e n\ x!=0 ; 1,\ \ \ \ w h e n\ x=0 . Show that f(x) is discontinuous at x=0 .

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.

Show that f(x)={1+x^2,if0lt=xlt=1 and 2-x if x >1 is discontinuous at x=1

If f(x)={(x^2+1", "x ne 1),(" "3 ", "x=1):} , then check whether the function f(x) is continuous or discontinuous at x=1

If f(x)={'x^2(sgn[x])+{x},0 Option 1. f(x) is differentiable at x = 1 Option 2. f(x) is continuous but non-differentiable at x = 1 Option 3. f(x) is non-differentiable at x = 2 Option 4. f(x) is discontinuous at x = 2

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

Show that the function f(x) given by f(x)={((e^(1/x)-1)/(e^(1/x)+1), when x!=0), (0, when x=0):} is discontinuous at x=0 .

If f(x) = (x + 1)/(x-1) and g(x) = (1)/(x-2) , then (fog)(x) is discontinuous at

If f(x) = (1)/(x^(2) - 17 x + 66) , then f((2)/(x - 2)) is discontinuous at x =