Explain why the following functions are continuous on the given open intervals:

Question

(a) f(x) = 3x^2 + 7 over
x − 4.
on (4,∞).

Answer 1

f(x) is continuous everywhere except at x=4, and the domain does not include x=4

and try just typing fractions normally, ok?
f(x) = (3x^2+7)/(x-4)

Answer 2

The function is discontinuous at x=4, but the given domain interval doesn't include x=4, so the function is continuous given the interval.