[" Let "f(x)" be defined in the interval "[0,4]],[" such that "f(x)={[1-x,,quad 0<=x<=1],[x+2,,1

Let f(x) be defined in the interval [0,4] such that f(x) ={{:(1-x,0lex le 1),( x+2, 1lt xlt2),( 4-x, 2 le x le 4):} , then the number of points where f(x) is discontinuous is (a) 1 (b) 2 (c) 3 (d) none of these

Let f(x) be defined in the interval [-2,2] such that f(x)={-1;-2<=x<=0} and f(x)={x-1;0

Let the function f(x)=x^2+x+s in x-cosx+log(1+|x|) be defined on the interval [0,1] .Define functions g(x)a n dh(x)in[-1,0] satisfying g(-x)=-f(x)a n dh(-x)=f(x)AAx in [0,1]dot

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) = e^x + sin x be defined on the interval [–4, 0]. Find the odd and even extension of f(x) in the interval [–4, 4].

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+sin x-cos x+log(1+|x|) be defined on the interval [0,1]. Define functions g(x) and h(x) in [-1,0] satisfying g(-x)=-f(x) and h(-x)=f(x)AA x in[0,1]

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)