Question

Hello! I need some assistance with this homework question, pleaseQ2

Answer 1

Recall that:

`(f\cdot g)(x)=f(x)g(x)\text{.}`

Then, if:

`\begin{gathered} x\in\text{Dom(f)}\cap Dom(g) \\ \text{then} \\ x\in\text{Dom(f}\cdot g)\text{.} \end{gathered}`

Now, notice that:

`\begin{gathered} x\in\text{Dom(f}\cdot g)\text{ if } \\ f(x)\text{ and g(x) exists,} \\ \text{then} \\ x\in\text{Dom(f)}\cap Dom(g). \end{gathered}`

Therefore:

`\text{Dom(f}\cdot g)=\text{Dom(f)}\cap Dom(g).`

Answer: True.