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

If a, b, c, d in R such that a lt b lt c lt d, then roots of the equation (x-a)(x-c)+2(x-b)(x-d) = 0

If a , b , c are real numbers, then find the intervals in which f(x)=|x+a^2a b a c a b x+b^2b c a c b c x+c^2| is increasing or decreasing.

If (x-a) (x-b) lt 0 , then x lt a, and x gt b .

If 1lt(x-1)/(x+2)lt7 then find the range of (i) x (ii) x^(2) (iii) (1)/(x)

If a ,\ b ,\ c are real numbers, then find the intervals in which f(x)=|(x+a^2,a b, a c),( a b, x+b^2,b c),( a c, b c, x+c^2)| is increasing or decreasing.

If f(x)=8-x^(2) where -3lt x lt3 , what is the range of values of f(x) ?

Let f(x) = {{:(-2 sin x,"for",-pi le x le - (pi)/(2)),(a sin x + b,"for",-(pi)/(2) lt x lt (pi)/(2)),(cos x,"for",(pi)/(2) le x le pi):} . If f is continuous on [-pi, pi) , then find the values of a and b .

Statement-1: If a, b, c, A, B, C are real numbers such that a lt b lt c , then f(x) = (x-a)(x-b)(x-c) -A^(2)(x-a)-B^(2)(x-b)-C^(2)(x-c) has exactly one real root. Statement-2: If f(x) is a real polynomical and x_(1), x_(2) in R such that f(x_(1)) f(x_(2)) lt 0 , then f(x) has at least one real root between x_(1) and x_(2)

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 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