If `f(x)={{:(x-2,xlt=0) , (4-x^2,x >0):} , discuss continuity of `y=f(f(x))

If f(x)=x-2, x le 0 and 4-x^2,x > 0, then discuss the continuity of y=f(f(x)).

Discuss the continuity of f(x)=sgn(x^2-2x+3)

Let f(x) ={{:(1+x,0lexle2),(3-x,2ltxle3):} then discuss the continuity of g(x) =f(f(x)).

if f(x) ={{:( x-1, xlt 0),( x^(2) - 2x , x ge 0):} , then

Prove that the function f(x)= {:{((sinx)/x , xlt 0), (x^(2)+1, x ge 0):} in x in RR is continuous

f(x)={|x+1|;xlt=0x ;x >0 and g(x)={|x|+1;xlt=1-|x-2|;x >1 Draw its graph and discuss the continuity of f(x)+g(x)dot

Let f(x)={{:(x^(2)+4,":",xlt0),(4-2x,":",xge0):} then the area bounded by y=f(x) and the x - axis from x=-1" to "x=3 is equal to

A function f(x) is defined by, f(x) = {{:(([x^(2)]-1)/(x^(2)-1)",","for",x^(2) ne 1),(0",","for",x^(2) = 1):} Discuss the continuity of f(x) at x = 1.

If f(x)={{:(2+x",", x ge0),(4-x",", x lt 0):}, then f (f(x)) is given by :

if f(x)={{:(2+x,xge0),(2-x,xlt0):} then lim_(x to 0) f(f(x)) is equal to (A) 0 (B) 4 (C) 2 (D) does not exist