19 24 Explain using Theorems 4 5 6 and 8 why the fun tion is continuous at every number in its domain State the domain no 19 F x 4 THEOREM If f and g are continuous at a and c is a constant then the following functions are also continuous at a 1 f g 2 f g f 4 fg g 2x x 1 x 1 5 c h x x if g a 0 5 THEOREM a Any polynomial is continuous everywhere that is it is continuous on R 0 0 b Any rational function is continuous wherever it is defined that is it is continuous on its domain EXAMPLE 6 On what intervals is each function continuous a f x x100 2x 7 75 x 1 x 1 3 cf b g x TAM OF x 1 x 1 User p x 2x 17 x 1 8 THEOREM If g is continuous at a and f is continuous at g a then the composite function fo q given by fog x f g x is continuous at a