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

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 : sqrt(3-x)+sin^-1((3-2x)/5)

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 of the following functions are defined : cosec^-1 3x

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

For which value of k will the following pair of linear equation have no solution? 3x+y=1, (2k-1)x+(k-1)y=2k+1

Prove the following: tan^-1x = sin^-1(frac{x}{sqrt(1+x^2)})

Find the product of the following. (x-8) (x+3) (x+1)