let f 01 01 be a continuous function show that there exists xsubzero 01 such that fxsubzeroxsubz

Name: let f 01 01 be a continuous function show that there exists xsubzero 01 such that fxsubzeroxsubzero 29478
Uploaded: 2023-07-06T03:30:35-08:00
Duration: 3 min 5 s
Channel: Madhur L
Description: let f 01 01 be a continuous function show that there exists xsubzero 01 such that fxsubzeroxsubzero 29478

Question

Audrey Fong · Accepted Answer

Step 1: Define a function g(x) = f(x) - x.

Question

Let f: [0,1] -> [0,1] be a continuous function. Show that there exists x₀ ∈ [0,1] such that f(x₀) = x₀.

Please give Ace some feedback