Define the discontinuity of `f(x)" at " x =a`

Find the number of integral discontinuities of f(x)=(tanx" " tan"^(-1)((1)/(x)-1))/(x(x-2)(x-4))

Number of point of discontinuity of f(x)=tan^2x-sec^2x in (0, 2pi) is _

Draw the graph and find the points of discontinuity for f(x)=[x^(2)-x-1],x in[-1,2] ([.] represents the greatest integer function).

Let f(x)=[sinx + cosx], 0ltxlt2pi , (where [.] denotes the greatest integer function). Then the number of points of discontinuity of f(x) is :

Draw the graph and find the points of discontinuity f(x) = [2cos x] , x in [0, 2pi] . ([.] represents the greatest integer function.)

A function phi(x) is defined as follows : phi(x)=2," when x is an integer" =0," when x is not an integer" Draw the graphs of the function and from the graph find the points of discontinuity of phi(x).

Let f (x) = [3+2 cos x] , x in (-frac(pi)(2),frac(pi)(2)) where [.] denotes the greatest integer function The number of points of discontinuity of f (x) is

Find all the points of discontinuity of f defined by f(x)= |x|-|x+1| .

Match the following for the type of discontinuity at x=1 in column II for the function in column I. f(x)=1/(x-1) , p. Removable discontinuity f(x)=(x^3-x)/(x^2-1) , q. Non-removable discontinuity f(x)=(|x-1|)/(x-1) , r. Jump of discontinuity f(x)=sin(1/(x-1)) , s. Discontinuity due to vertical asymptote , t. Missing point discontinuity , u. Oscillating discontinuity

The number of points of discontinuity of g(x)=f(f(x)) where f(x) is defined as, f(x)={1+x ,0lexle2 3-x ,2ltxle 3