Question

Let f: [0,1] -> [0,1] be a continuous function. Show that there exists xsubzero [0,1] such...

Let f: [0,1] -> [0,1] be a continuous function. Show that there exists xsubzero [0,1] such that f(xsubzero)=xsubzero

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let f: (0,1) -> R be uniformly continuous and let Xn be in (0,1) be such...
Let f: (0,1) -> R be uniformly continuous and let Xn be in (0,1) be such that Xn-> 1 as n -> infinity. Prove that the sequence f(Xn) converges
Let f be a continuous function. Suppose theres a sequence (x_n) in [0,1] where lim f(x_n))=5....
Let f be a continuous function. Suppose theres a sequence (x_n) in [0,1] where lim f(x_n))=5. Prove there is a point x in [0,1] where f(x)=5.
Let f : [1, 2] → [1, 2] be a continuous function. Prove that there exists...
Let f : [1, 2] → [1, 2] be a continuous function. Prove that there exists a point c ∈ [1, 2] such that f(c) = c.
Let a > 0 and f be continuous on [-a, a]. Suppose that f'(x) exists and...
Let a > 0 and f be continuous on [-a, a]. Suppose that f'(x) exists and f'(x)<= 1 for all x2 ㅌ (-a, a). If f(a) = a and f(-a) =-a. Show that f(0) = 0. Hint: Consider the two cases f(0) < 0 and f(0) > 0. Use mean value theorem to prove that these are impossible cases.
Let f : R → R be a continuous function which is periodic. Show that f...
Let f : R → R be a continuous function which is periodic. Show that f is bounded and has at least one fixed point.
Prove that the function f(x) = x2 is uniformly continuous on the interval (0,1).
Prove that the function f(x) = x2 is uniformly continuous on the interval (0,1).
Show the following: a) Let there be Y with the cumulative distribution function F(y). Let F(Y)=Z....
Show the following: a) Let there be Y with the cumulative distribution function F(y). Let F(Y)=Z. Show that Z~U(0,1) for F(y). b) Let X~U(0,1), and let Y := -ln(X). Show that Y~exp(1)
Show there does not exist a sequence of continuous functions fn : [0,1] → R converging...
Show there does not exist a sequence of continuous functions fn : [0,1] → R converging pointwise to the function f : [0,1] → R given by f(x) = 0 for x rational, f(x) = 1 for x irrational.
Let f : [a,b] → R be a continuous function such that f(x) doesn't equal 0...
Let f : [a,b] → R be a continuous function such that f(x) doesn't equal 0 for every x ∈ [a,b]. 1) Show that either f(x) > 0 for every x ∈ [a,b] or f(x) < 0 for every x ∈ [a,b]. 2) Assume that f(x) > 0 for every x ∈ [a,b] and prove that there exists ε > 0 such that f(x) ≥ ε for all x ∈ [a,b].
prove that this function is uniformly continuous on (0,1): f(x) = (x^3 - 1) / (x...
prove that this function is uniformly continuous on (0,1): f(x) = (x^3 - 1) / (x - 1)