Find the value of x for which
`f(x) = ((x-2)^(2)(1-x)(x-3)^(2)(x-4)^(2))/((x-1))le 0.`

find the value of x for which f(x) = ((2x-1)(x-1)^(2)(x-2)^(2))/((x-4)^(2))ge 0.

Find the value of 'a' for which the function f defined as f(x) = {(a sin""(pi)/(2)(x+1)",",x le 0),((tan x - sin x)/(x^(3))",", x gt 0):} is continuous at x = 0.

Find the range of the following functions (i) f(x) = log_(2)(sqrt(x-4) + sqrt(6-x)), 4 le x le 6 (ii) f(x) = 9^(x) - 3^(x) + 1

If f(x)=x^2+x+1 , then find the value of 'x' for which f(x-1) =f(x)

Find the range of function, f: [0,1] -> R, f(x)= x^3-x^2+4x+2sin^-1x .

Find the value of k , so that the function f(x) = {(kx^2 + 5, if x le 1), (2, if x gt 1):} is continuous at x = 1

Find the value of k, so that the function f(x) = {(kx^2 + 5, if x le 1), (2, if x gt 1):} is continuous at x = 1

Let f(x)=((x-1)^(3)(x+2)^(4)(x-3)^(5)(x+6))/(x^(2)(x-7)^(3)) . Solve the following inequality f(x)le0

Let f (x) be a continous function in [-1,1] such that f (x)= [{:((ln (ax ^(2)+ bx +c))/(x ^(2)),,, -1 le x lt 0),(1 ,,, x =0),((sin (e ^(x ^(2))-1))/(x ^(2)),,, 0 lt x le 1):} Then which of the following is/are corrent

Find the inverse of each of the following functions : f(x) = {{:(x"," -oo lt x lt 1),(x^(2)"," 1 le x le 4),(2x"," 4 lt x lt oo):}