First recall that [tex]\sin^{-1}x[/tex] is defined only for [tex]-1\le x\le1[/tex], which means [tex]\sin^{-1}(x+3)[/tex] requires that [tex]2\le x+3\le4[/tex].
Over this domain, [tex]\sin^{-1}(x+3)[/tex] will be invertible, and so taking the sine of both sides, we have
