Using the properties of combinations of continuous functions, determine the interval(s) over which the function f(x)=x²√x+12 is continuous. O O a.) [12, ∞) b.) (-∞, ∞) c.) [-12, ∞) d.) (-∞, -12]

|Determine whether the statement is true or false. Prove the statement if it is true, and give a counterexample if it is false. (i) For all real numbers x and y, [x – y] = [x] – [y]. | (ii) Let a, b and c be integers. If a|(bc), then a|6 or alc.

Give your answer in interval notation

Fill in the blank with the correct choice. Suppose f(x) is decreasing over the interval [7, 13], and f(7)=20. Then the value of f(13) none of these will be more than 120 O will be less than is about the same as f(7) 20.

Determine the intervals on which the given function is concave up or concave down and find the points of inflection. f(x) — 2хе-9х (Use symbolic notation and fractions where needed. Give your answer as a comma separated list of points in the form in the form (*, *). Enter DNE if there are no points of inflection.) points of inflection: Determine the interval on which f is concave up. (Use symbolic notation and fractions where needed. Give your answer as interval in the form (*, *). Use the symbol o for infinity, U for combining intervals, and an appropriate type of parenthesis "(", ")", "[", "]" depending on whether the interval is open or closed. Enter Ø if the interval is empty.) x E