Determining Continuity Examples

Let f(x) = 4x² + 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) = 4x² + 3x = x(4x + 3).

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