Range of f(x)

such functions are known as restricted functions..

here sin^-1x and cos^-1x are res. funcs as have restrcted domains from -1 to 1

thus, -1 < x < 1

now, f(x) = sin^-1x2 + cos^-1x3 + tan^-1x4

= (6sin^-1x + 4cos^-1x + 3tan^-1x)/12 = (2sin^-1x + 3tan^-1x + 2pi)/12

now, on diff. we can easily find the min val. and max val. of the expression...