Which statement best justifies that the function h(x)=sin(3x2+6) is continuous for all real numbers?
a) Because sin(3x2+6) contains no denominators or square-roots, there are no points where it is undefined, so it is continuous.
b) Because sinx is differentiable everywhere, its composition with any function is automatically continuous.
c) Because both sinx and the polynomial 3x2+6 are continuous everywhere, and the composition of two continuous functions is continuous.
d) Because the range of sinx is bounded between −1 and 1, eliminating discontinuities.