Let f(x) be defined in the interval [-2,2] such that `f(x) = { -1; -2<= x <= 0} and f(x) = {x-1 ; 0 < x <=2}` and `g(x) = f(|x|) + |f(x)|`, The number of points where g(x) is not differentiable in (-2,2), is

Let f(x) be defined in the interval [-2,2] such that f(x)=-1 for -2<=x<0 and 1-x for 0<=x<2.g(x)=f(|x|)+|f(x)| The number of points where g(x) is not differentiable in (-2, 2),is

Let f be a real -valued function defined on the interval (-1, 1) such that e^(-x)f(x) = 2+int_(0)^(x) sqrt(t^(4) + 1)dt for all x in (-1, 1) and let f^(-1) be the inverse function of f. then show that (f^(-1)(2))^1 = (1)/(3)

Let f be a real valued function defined on the interval (-1,1) such that e^(-x) f(x) = 2 + int_0^x sqrt(t^4 + 1) dt , for all x in (-1, 0) and let f^(-1) be the inverse function of f. Then (f^(-1))'(2) is equal to :

Let f(x) be defined on [-2,2[ such that f(x)={{:(,-1,-2 le x le 0),(,x-1,0 le x le 2):} and g(x)= f(|x|)+|f(x)| . Then g(x) is differentiable in the interval.

Let f(x)=x^(2)+x be defined on the interval [0,2). Find the odd and even extensions of f(x) in the interval [-2,2] .

Let the function f(x)=x^(2)+x+sinx- cosx+log(1+|x|) be defined on the interval [0,1]. The odd extension of f(x) to the interval [-1,1] is

Let the function f(x)=x^(2)+x+sinx- cosx+log(1+|x|) be defined on the interval [0,1]. The odd extension of f(x) to the interval [-1,1] is

Let f(x) be defined on [-2,2] and is given by f(x) = {{:(x+1, - 2le x le 0 ),(x - 1, 0 le x le 2):} , then f (|x|) is defined as