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 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 : sin^-1(x^2-3x+1)

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

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 k for which the function f : R rarr R defined by f(x)=5+kx,kne0 is the inverse of itself.

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 range of the following functions given by : f(x)=|x-3|

Find the range of the following functions given by : f(x)=1-|x-2|