Show that a continuous function f : [0, 1] → Z is a constant function.

Q: Let f : R R:f(x) = 10x + 7. Find the function g : R→R such that gof = fog = IR. %3D %3D

A: Given f: R -> R  such that f(x) = 10x + 7 and  g : R -> R such that g o f = f o g = IR

Q: Suppose that g is a continuous function. Find the general solution of y" – y = g(t).

A:

Q: Assume that a continuous function f:R → R is X- and µ-periodic, where A and u are two nonzero…

A: We know that between two rational number lies infinite many irrational number. But function is…

Q: Let f be continuous from [0, 1] to [0, 1]. By posing 6(x) = f(x) – x, show that fhas a fixed point…

A:

Q: Suppose that f(x) is a continuous function on [a , b] and F(x)= | f(t) dt a Part 1 of the…

A:

Q: Let f: R³ R be the function defined as f(x, y, z)= √√₂² + y² + 2², 0. if (x, y, z) = Q³, otherwise.…

A:

Q: Theorem 11. Let f be a continuous function on R such that f(x+y)-f(x)+fv) vx, yER. Show that f(x)3cx…

A:

Q: Let X be Hausdorff and f : X → X be a continuous function. Show that {x : f (x) = x} is closed in X.

A: Let, .We show  is open and so F is closed.

Q: Let f(x) = V5x² – 20. Find everywhere f is continuous. -

A: Given fx=5x2-20

Q: b) Give an example of a function g: R →R that is continuous at some xE R, but not differentiable at…

A:

Q: Let f: S¹→ S¹ be a continuous function. Proof or disprove the following statements : a) f has a…

A: Given that the  function f : S1 → S1 be a continuous function  where S1 = x,y∈ℝ2 : x2 + y2  =1 We…

Q: Show that the function f: C → C given by f(z) = z2 is continuous on C.

A:

Q: "Prove that the function f : R→ R with ƒ(x) = = is uniformly continuous."

A:

Q: Let f : Z+ → N be the floor function f(x) = [(x – 1)/2].

A:

Q: If a function f: D R is differentiable at a point (a, b)ED, then f is continuous at (a, b);

A:

Q: Let f(x) = |x|+|x−2], x € R. Find points where f is not differentiable.

A:

Q: Let h : R → R be some twice-differentiable function. Define f(x,y) = h(x) for all x ≠ 0. Show that…

A:

Q: 2. Determine if a function f : [0, 27] → R defined by f(x) = sin 2n is continuous.

A:

Q: Let f: RR be a function satisfying f(x + y) = f(x) + f(y) for all x, ye R. If the function f(x) is…

A: Note :   Let r>0 and c∈R ,then vr(c)={x∈R : x-c<r }=(c-r ,c+r) ,which is called r…

Q: (b) Let X = (a, b]. Construct a continuous function f : X → R (set of real numbers) which is…

A:

Q: f(x) = {*- Įx² +px + 2,x # 3 3, x = 3

A:

Q: q17. Let f, g, h be continuous functions on an interval [a, b]. If f is orthogonal to g and to h,…

A:

Q: 4. Give an example of a continuous function f : (0, 1) → R that cannot be uniformly approximated by…

A:

Q: Suppose that the function f: [0, 1] in R is continuous and thatf(x) > 2      if 0<=X < 1.Is…

A:

Q: Show that the function f(z) = z is nowhere analytic on C.

A:

Q: 4. Let f:R→ R be a function defined by f(x)=x for every xeX . Show that f is a continuous.

A: Let A ⊆ R , let f:A → R and let c ∈ A. We say that f is continuous at c if, given any number ε>0,…

Q: Give an example of a continuous function f : C -> C, where f is holomorphic at 0 but no other point…

A:

Q: Rewrite the following integral using the indicated order of integration and then evaluate the…

A:

Q: Define the function zlm(z) z +0 f(2) = Z = 0 1. Prove that f is continuous at the origin. 2. Prove…

A: This question is related to complex analysis . Topic is continuity and differentiability.

Q: 3. Let f [2,3] → {1,3} be a continuous function such that the equation f(x) - x = 0 has a solution a…

A: 3 Give that f:2,3→1,3 be a continuous function such that the equation fx-x=0 has a solution x in…