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 the following are defined : sin^-1(x^2-3x+1)

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^-1frac{x}{2}+sec^-1 x

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

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

Find the values of a and b for which the following system of linear equation has infinitely many solutions. (2a-1)x-3y=5, 3x+(b-2)y=3

Find the roots of the following quadratic equation x^2-5sqrt3x+18=0

Find the roots of the following quadratic equation 3x^2-4sqrt3x+4=0

Find the value of a for which the function f(x) = a sin x + (1)/3 sin 3x has an extremum at x =pi/3 .

Find the domain of the following functions given by f(x)=1/sqrt(2-x)(x-3)