If `f(x) = {{:(x - 3",",x lt 0),(x^(2)-3x + 2",",x ge 0):}"and let" g(x) = f(|x|) + |f(x)|`. Discuss the differentiability of g(x).

Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

Let f(x) be defined on [-2,2] and be given by f(x)={(-1",",-2 le x le 0),(x-1",",0 lt x le 2):} and g(x)=f(|x|) +|f(x)| . Then find g(x) .

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

Number of points where f (x)= {{:(max(|x ^(2)- x-2|","x ^(2) -3x),,, x ge0),( max (ln (-x)"," e ^(x)),,, x lt 0):} is non-differentiable will be:

Let f(x)={(x^(2)-4x+3",",x lt 3),(x-4",",x ge 3):} and g(x)={(x-3",",x lt 4),(x^(2)+2x+2",",x ge 4):} . Describe the function f//g and find its domain.

Let f(x)={(x^(2)-4x+3",",x lt 3),(x-4",",x ge 3):} and g(x)={(x-3",",x lt 4),(x^(2)+2x+2",",x ge 4):} . Describe the function f//g and find its domain.

If f(x) = {sinx , x lt 0 and cosx-|x-1| , x leq 0 then g(x) = f(|x|) is non-differentiable for

Let f(x)={{:(x sin.(1)/(x)",",x ne0),(0",",x=0):}} and g(x)={{:(x^(2)sin.(1)/(x)",", x ne 0),(0",", x=0):}} Discuss the graph for f(x) and g(x), and evaluate the continuity and differentiabilityof f(x) and g(x).

f(x)={(log_(e)x",",0lt x lt 1),(x^(2)-1 ",",x ge 1):} and g(x)={(x+1",",x lt 2),(x^(2)-1 ",",x ge 2):} . Then find g(f(x)).

f(x)=x^x , x in (0,oo) and let g(x) be inverse of f(x) , then g(x)' must be