Find the values of x for which the following are defined : `cos^-1(2/(2+sinx))`

Find the values of x for which the following are defined : sin^-1(x^2-3x+1)

Find the values of x for which of the following functions are defined : cos^-1 (x^2-5x+5)

Find the values of x for which the following are defined : sin^-1frac{x}{2}+sec^-1 x

Find the values of x for which the following are defined : sqrt(3-x)+sin^-1((3-2x)/5)

Find the values of x for which of the following functions are defined : cosec^-1 3x

Find the value of x for which the following expressions are minimum. Also determine their minimum values. x^2-6x+40 .

Find the value of x for which the following expressions are minimum. Also determine their minimum values. 4x^2-12x+13 .

Find the values of a and b for which the following system of linear equation has infinitely many solutions. (a-1)x+3y=2, 6x+(1-2b)y=6

Find the values of a and b for which the following system of linear equation has infinitely many solutions. 2x-(2a+5)y=5, (2b+1)x-9y=15

Find the value of x for which the following expressions aquire greatest value ? Also determine their greatest values. 24x-8-9x^2 .