What are the regions of continuity given the following?

or each of the following functions R → R, say if it is continuous in the cofinite topology.You do not need to justify your answer.(a) f (x) = x2 + 2x + 5 [2,U]It is continuous because |f −1(a)| ≤ 2 for all a ∈ R.(b) g(x) = sin(x + 2) [2,U]It is not continuous because |g−1(0)| = ∞.(c) h(x) = e3x [2,U]It is continuous because |h−1(a)| ≤ 1 for all a ∈ R

Consider the function f : R2 → R defined byf (x, y) =cos x sin yy if y̸ = 0cos x if y = 0.Is f continuous everywhere? Justify your answer.(b) Let g : R2 → R be defined byg(x, y) =2xy x2 − y2x2 + y2 if (x, y)̸ = (0, 0)a if (x, y) = (0, 0).(i) (2 marks) For what value(s) of a, if any, is g continuous at (0, 0)?

Which of the following functions is continuous for every value of x except x=0?

Which of the following is not continuous for all x

Using the properties of combinations of continuous functions, determine the interval(s) over whichthe function f(x) = x²-3x-18 x+2 is continuous.A. (-∞,-2)U(-2,00)B. (-2,2)C. (-8,08)D. (-0,-3)U(-3,-2)U(-2, 6) U (6,0∞)