continuous function
let f: R->R be a continuous function such that f(0)=f(2)=1. then there exists c>0 such that f(c)=c
prove this.
Answer
Answers can only be viewed under the following conditions:
- The questioner was satisfied with and accepted the answer, or
- The answer was evaluated as being 100% correct by the judge.
Erdos
4.8K
The answer is accepted.
Join Matchmaticians Affiliate Marketing
Program to earn up to a 50% commission on every question that your affiliated users ask or answer.
- answered
- 845 views
- $4.00
Related Questions
- Define $F : \mathbb{R}^ω → \mathbb{R}^ω$ by $F(x)_n = \sum^n_{k=1} x_k$. Determine whether $F$ restricts to give a well-defined map $F : (\ell_p, d_p) → (\ell_q, d_q)$
- Prove the uniqueness of a sequence using a norm inequality.
- real analysis
- $\textbf{I would like a proof in detail of the following question.}$
- What is the Lebesgue density of $A$ and $B$ which answers a previous question?
- Find $\lim\limits _{n\rightarrow \infty} n^2 \prod\limits_{k=1}^{n} (\frac{1}{k^2}+\frac{1}{n^2})^{\frac{1}{n}}$
- True-False real analysis questions
- Does the sequence $f_n=\arctan (\frac{2x}{x^2+n^3})$ converge uniformly on $\mathbb{R}$?