If `f ''(x)|le 1 AA x in R, and f (0) =0=f' (0),` then which of the following can not be true ?

Let f (x) =ax ^(2) + bx+ c,a gt = and f (2-x) =f (2+x) AA x in R and f (x) =0 has 2 distinct real roots, then which of the following is true ?

Let f (x) =ax ^(2) + bx+ c,a gt = and f (2-x) =f (2+x) AA x in R and f (x) =0 has 2 distinct real roots, then which of the following is true ?

Le f : R to R and g : R to R be functions satisfying f(x+y) = f(x) +f(y) +f(x)f(y) and f(x) = xg (x) for all x , y in R . If lim_(x to 0) g(x) = 1 , then which of the following statements is/are TRUE ?

If f(x)=int_(0)^(x)(e^(t)+3)dt , then which of the following is always true AA x in R

Let f be a function on R given by f(x) = x^(2) and let E = {x in R: - 1 le x le 0 } and F = { x in R , 0 le x le 1 } then which of the following is fase ?

If 0ltalt1 and f is defined as f(x)={[x^(a),x>0],[0,x=0]} ,then which of the following is true.

If f(x+k) + f(x) = 0 AA x in R and k in R^(+) , then the period of f(x) is

f(x)={(x-1",",-1 le x le 0),(x^(2)",",0le x le 1):} and g(x)=sinx Consider the functions h_(1)(x)=f(|g(x)|) and h_(2)(x)=|f(g(x))|. Which of the following is not true about h_(1)(x) ?