Find the domain

Question

𝐿𝑒𝑡 𝑓(𝑥) = {

3𝑥

2𝑆𝑖𝑛 1

𝑥

𝑖𝑓 𝑥 ≠ 0

0 𝑖𝑓 𝑥 = 0

(a) 𝐹𝑖𝑛𝑑 𝑡ℎ𝑒 𝑑𝑜𝑚𝑎𝑖𝑛 𝐷𝑓 𝑜𝑓 𝑓(𝑥).

Answer 1

I think that this is something like what you meant

in which case the domain is all real numbers since the function will approach zero on either sido of zero and at zero it will be be 0 from the piece wise component.