`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`

Discuss the continuity of f(x)={1/(e^(x-1)),x!=1 0,x=1

Draw and discuss the graph of f(x) = x+sqrt(x-1)

If f(x)=(x+1)/(x-1)a n dg(x)=1/(x-2),t h e n discuss the continuity of f(x),g(x),a n dfog(x)dot

If f(x) = {|x|-|x-1|}^(2) , draw the graph of f(x) and discuss its continuity and differentiability of f(x)

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

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

Let f(x)={x+1,x >0, 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

Let f(x)={x+1,x >0 \n 2-x ,xlt=0 and g(x)={x+3,x 0)g(f(x)).

if f(x) ={{:(x+2 ,if xlt0),(-x^(2)-2 ,if 0le xlt1),( x ,if xge1):} then the number of points of discontinuity of |f(x)|is (a) 1 (b) 2 (c) 3 (d) none of these

Let f (x) = x^3-x^2-x+1 and g(x) = {max{f(t); 0<=t<=x}, 0<=x<=1, 3-x, 1<=x<=2 Discuss the continuity and differentiability of the function g (x) in the interval (0, 2).