Question

Let f : [0, 1] → R be continuous with [0, 1] ⊆ f([0, 1]). Show...

Let f : [0, 1] → R be continuous with [0, 1] ⊆ f([0, 1]). Show that there is a c ∈ [0, 1] such that f(c) = c.

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let 0 < a < b < ∞. Let f : [a, ∞) → R continuous...
Let 0 < a < b < ∞. Let f : [a, ∞) → R continuous R at [a, b] and f decreasing on [b, ∞). Prove that f is bounded above.
. Let f and g : [0, 1] → R be continuous, and assume f(x) =...
. Let f and g : [0, 1] → R be continuous, and assume f(x) = g(x) for all x < 1. Does this imply that f(1) = g(1)? Provide a proof or a counterexample.
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.
Show that a continuous injective map f: (0, 1) to R is an embedding.
Show that a continuous injective map f: (0, 1) to R is an embedding.
Let f: [a,b] to R be continuous and strictly increasing on (a,b). Show that f is...
Let f: [a,b] to R be continuous and strictly increasing on (a,b). Show that f is strictly increasing on [a,b].
4a). Let g be continuous at x = 0. Show that f(x) = xg(x) is differentiable...
4a). Let g be continuous at x = 0. Show that f(x) = xg(x) is differentiable at x = 0 and f'(0) = g(0). 4b). Let f : (a,b) to R and p in (a,b). You may assume that f is differentiable on (a,b) and f ' is continuous at p. Show that f'(p) > 0 then there is delta > 0, such that f is strictly increasing on D(p,delta). Conclude that on D(p,delta) the function f has a differentiable...
Let f, g : [a, b] ---> R continuous such that (f(a) - g(a)) (f(b) -...
Let f, g : [a, b] ---> R continuous such that (f(a) - g(a)) (f(b) - g(b)) < 0. b) Show that inf {|f(x) - g(x)| : x ϵ [a,b]} = 0 and is achieved (is a minimum).
Let f, g : [a, b] ---> R continuous such that (f(a) - g(a)) (f(b) -...
Let f, g : [a, b] ---> R continuous such that (f(a) - g(a)) (f(b) - g(b)) < 0. a) Show that sup{|f(x) - g(x)| : x ϵ [a, b]} is strictly positive and achieved (is a maximum).
Let f: R --> R be a differentiable function such that f' is bounded. Show that...
Let f: R --> R be a differentiable function such that f' is bounded. Show that f is uniformly continuous.
Let f: [0, 1] --> R be defined by f(x) := x. Show that f is...
Let f: [0, 1] --> R be defined by f(x) := x. Show that f is in Riemann integration interval [0, 1] and compute the integral from 0 to 1 of the function f using both the definition of the integral and Riemann (Darboux) sums.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT