If `f(x)` is defined on `[-2, 2]` and is given by
`f(x)={{:(-1",",-2lexlt0),(x-1",",0ltxle2):} and g(x)=f|x|+|f(x)|`, then `g(x)` is defined as

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

If a function f(x) is defined as f(x) = {{:(-x",",x lt 0),(x^(2)",",0 le x le 1),(x^(2)-x + 1",",x gt 1):} then a. f(x) is differentiable at x = 0 and x = 1 b. f(x) is differentiable at x = 0 but not at x = 1 c. f(x) is not differentiable at x = 1 but not at x = 0 d. f(x) is not differentiable at x = 0 and x = 1

A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0):} , then f(x) is

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).

If ‘f' is defined by f(x) = x^2 , find f' (2).

Let f:R rarr R be defined by f(x)={{:(2x, xgt3),(x^2,1lexlt3),(3x,xle1):} Then f(-1)+f(2) +f(4) is

If the function f is defined by f(x)={(7" , "xne0),(a-1" , "x=0):} and f is continuous at x=0 then value of 'a' is _____

Let g(x)=f(x)+f(1-x) and f''(x)<0 , when x in (0,1) . Then f(x) is