Let f(x) = 4x^{2} + 3x and g(x) = sin(x). Determine whether each function is continuous. If not, where is the function discontinuous?

(f + g)

(f – g)

(f + g) is continuous, since both f and g are continuous.

(f – g) is continuous, since both f and g are continuous.

is continuous wherever g is not zero. g is zero at all multiples of π (0,π, -π, 2π,-2π, ...). will be continuous on the intervals ..., (-2π, -π), (-π,0), (0,π), (π,2π),...

is continuous wherever f is not zero. f(x) = 4x^{2} + 3x = x(4x + 3).

Since f is zero when x = 0 and when , the function is continuous on the intervals