Question

Square of f is continuous functions proof in analysis

Answer 1

Answer:

Step-by-step explanation:

Prove that if f is defined for x≥0 by f(x)=x−−√, then f is continuous at every point of its domain.

Definition of a continuous function is:

Let A⊆R and let f:A→R. Denote c∈A.

Then f(x) is continuous at c iff for every ε>0, ∃ δ>0 such that

|x−c|<δ⟹|f(x)−f(c)|<ε.

My attempt:

We know that the function f:x→R, where x∈[0,∞) is defined to be f(x)=x−−√. So, for 0≤x<∞, then |f(x)−f(c)|=|x−−√−f(c)| and I can't continue since I don't necessarily know what c is in this case.