Let `f(x)={x ; x<0 and 1-x ; x>=0 and g(x)+{x^2 ; x<-1 and 2x+3 ; -1<=x<=1 and x ; x>1` ; On the basis of above information, answer the following questions Range of `f(x)` is

If f(x)=|x-3|+2|x-1| and g(x)=-2x^(2)+3x-1 On the basis of above information answer the following questions: Minimum value of f(x) is

Let f : R -> R is a function satisfying f(2-x) = f(2 + x) and f(20-x)=f(x),AA x in R . On the basis of above information, answer the following questions If f(0)=5 , then minimum possible number of values of x satisfying f(x) = 5 , for x in [0, 170] is

If f(x) is a monic polynomial of degree '3' such that lim_(x to 0) (1+f(x))^(1/(x^(2)))=e^(-3), g(x)=(f(x))/(x^(3))dx and g(1)=1 then On the basis of above information, answer the following question: Value of g(e) is

In a problem of differentiation of (f(x))/(g(x)) , one student writes the derivative of (f(x))/(g(x)) as (f'(x))/(g'(x)) and he finds the correct result . If g(x)=x^(2)and lim_(xtooo) f(x)=4 On the basis of above information , answer the following questions : The function f(x) is

Let there are two functions defined of f(x)="min"{|x|,|x-1|,|x+1+] and g(x)="min"{e^(x),e^(-x)} on the basis of above information answer the following question: Number of solutions of f(x)=g(x) in the interval [0,1] is

Let f,g, h be 3 functions such that f(x)gt0 and g(x)gt0, AA x in R where int f(x)*g(x)dx=(x^(4))/(4)+C and int(f(x))/(g(x))dx=int(g(x))/(h(x))dx=ln|x|+C . On the basis of above information answer the following questions: int f(x)*g(x)*h(x)dx is equal to

If f(x)=(x-2)|x-4| sgn(x)AA x in R (Where sgn( x ) denotes signum function) On the basis of above information answer the following questions: f(x) is monotonically increasing in interval-

If f(x)=(x-2)|x-4| sgn(x)AA x in R (Where sgn( x ) denotes signum function) On the basis of above information answer the following questions: f(x) is monotonically increasing in interval-

Let there are two functions defined of f(x)="min"{|x|,|x-1|} on the basis of above information answer the following question: Points of non-differentiability of f(x) in (-1,1)