b) Prove that if f(z) and f(Z) are analytic in a domain I, then I is a constant function.

Q: Are the following functions quasi-concave? Assume x ≥ 0 a) f(x) = a b) f(x) = a + cx², c < 0

A: Both questions are different so I soved 1st queation if you want 2nd one then repost it again.

Q: 3. Prove if the function f : R → R is defined by the rule f (x) = 4.x + 1 for all real numbers x,…

A:

Q: Draw a function f(x), defined for all real numbers x, with one local maximum and two local minimum.

A:

Q: Viewed as a function f: R → R, a polynomial of odd degree is always surjective. True False

A:

Q: For a function f: A --> B and subsets C and D of A and E and F of B, prove that the relationship is…

A:

Q: If f is analytic in a neighborhood of ro and f(xo) = 0, show that f(r)/(x – ro) is analytic in the…

A: Analyticity

Q: Draw a function f(z), defined for all real numbers z, with two local maximum and one local minimum.

A: We will draw a function which has two local maximum and one local minimum.

Q: Determine the zeros of the function f(x) = -x¹ + x² +1. O a) There are no zeros. O b) x = -1.27 and…

A: GIVEN POLYNOMAIAL EQUATION  f(x)=-x4 +x2 +1

Q: Viewed as a function f: R → R, a polynomial of even degree is never injective. True False

A:

Q: 1. Describe all functions f such that f(r) ar² + bx +c and f(1) = 2 and f(-1) = 6.

A:

Q: Let B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3) Show that the function g is surjective.…

A: We are given that B = R − {3}. Define g : B → B by g(t) = 3t/(t − 3). We need to show that g is…

Q: 3. (a) Prove that the function f : R → R, ƒ(x) = 4x² −14x¹+30x-17, is injective. (b) Find the…

A: The answer to this question is given below.Explanation:

Q: Show that the function Arg(z) is not continuous on each point of the non-positive real axis.

A: