Question

A function f:X→Y maps each x∈X to some y∈Y. So consider tanπ2 for which tan(x) is undefined, so in this case, tan(x) does not map to an element of its range. This conflicts with my understanding of what a function is. Why do we still consider tan(x) a function?

Answer 1

Answer:

Step-by-step explanation:

Since any function which is continuous on a closed and bounded interval is uniformly continuous, in that way the given function is uniformly continuous.

And in the ϵ,δ method I tried this much. For x,y∈[0,π/4] |x−y|≤π/4(=δ)⟹|f(x)−f(y)|=|tanx−tany|=|sin(x−y)cosx.cosy|≤1=ϵ Then choosing δ=πϵ/4 , we have uniformly contnuity of the function. Should I do anything more?