Suppose that f : R →R is continuous and that its image f(R) is bounded. Prove that there is a solution of the equation f(r) = x, r in R.

At what points (x,y,z) in space are the functions continuous? a. h(x,y,z)= In (z³ - 4x³ - 3y³ - 2) 1 b. h(x,y,z) = z³-√x³+y³ a. At which points is h(x,y,z) = In (z3 - 4x³ - 3y³ - 2) continuous? Choose the correct answer below. O A. All points except (0,0,0) OC. All points satisfying z³ - 4x³ #3y³ - 2 3 O E. All points satisfying z3 - 4x³ - 3y³ √x³ + y² 3 3 3 3 3 All points satisfying z³ #√√x³ +y 3 continuous? Choose the correct answer below. MacBook Pro OB. All points satisfying z³ - 4x³ - 3y³ > 2 в. O D. All points satisfying x#y#z OF. All points satisfying z³ - 4x³ - 3y³ #2 O H. No points OB. All points satisfying x#y#z O D. All points satisfying x³ +y³ > 0 OF. 3 3 All points satisfying x³ + y³ ≥0 and OH. No points z³ #√√x 3 z³ # 3 3 +

Find all entire functions f(z)=u(x,y)+i(x,y) such that u(x,y) is not equal to zero for all (x,y) and that g(z)=(u(x,y))2+i(v(x,y))2 is also entire.

Find the analytic functiopn f (z) = u (x,y) + i ( x, y ) such that u ( x, y)=  4xy3-4x3y+x.