If `a lt b lt c `, then find the range of `f(x)="|x-a|+|x-b|+|x-c|`

if a lt c lt b, then check the nature of roots of the equation (a -b)^(2) x^(2) + 2(a+ b - 2c)x + 1 = 0

If c lt a lt b lt d , then roots of the equation bx^(2)+(1-b(c+d)x+bcd-a=0

If 3-((x^2)/(12))lt=f(x)lt=3+((x^3)/9) for all x!=0, then find the value of ("lim")_(xvec0)f(x)

If a lt b lt c lt d , then for any real non-zero lambda , the quadratic equation (x-a)(x-c)+lambda(x-b)(x-d)=0 ,has

If a ,b ,c in R , then find the number of real roots of the equation =|x c-b-c x a b-a x|=0

Find the values of a and b such that the function defined by f(x)={{:(5," if "x le 2),(ax+b," if "2 lt x lt 10),(21," if "x ge 10):} is a continuous function.

Let f(x)=ax^(2)+bx+c , a ne 0 , a , b , c in I . Suppose that f(1)=0 , 50 lt f(7) lt 60 and 70 lt f(8) lt 80 . Number of integral values of x for which f(x) lt 0 is

Let A, B, C in N and a function f:A to B be defined by f(x)=2x+1 and g: B to C be defined by g(x)=x^(2) . Find the range of fog and gof.