If `f(x)={|x|-3 x < 1|x-2|+a x >= 1 & g(x)={2-|x| x < 2 sgn(x)-b x >= 2. if h(x)=f(x)+g(x)` is discontinuous at exactly one point, then -

Let f(x)={{:(,|x|-3,x lt 1),(,|x-2|+a,x ge 1):} g(x)={{:(,2-|x|,x lt 1),(,Sgn(x)-b,x ge 1):} If h(x)=f(x)+g(x) is discontinuous at exactly one point, then which of the following are correct?

Let f(x)={x^(2)-4x+3,x =3} and g(x)={1,x = then function f(x)g(x) is discontinuous at (a)exactly 1 point (b) exactly 2 points (c)exactly 3 points (d) None of these

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

If f(x)=(1)/((1-x)) and g(x)=f[f{f(x))} then g(x) is discontinuous at

Let f(x)=sgn(x) and g(x)=x(x^(2)-5x+6) The function f(g(x)) is discontinuous at

Let f(x)=-x^(2)+x+p , where p is a real number. If g(x)=[f(x)] and g(x) is discontinuous at x=(1)/(2) , then p - cannot be (where [.] represents the greatest integer function)

If f (x) = 3x -1, g (x) =x ^(2) + 1 then f [g (x)]=

If f(x) = 3x + 1 and g(x) = x^(2) - 1 , then (f + g) (x) is equal to

The function f(x) : (x-1)/(x( x^(2) -1)) is discontinuous at (a) exactly one point (b) exactly two points (c) exactly three points (d) no point