VanniaV229986 VanniaV229986
  • 03-11-2022
  • Mathematics
contestada

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

Hello I need some assistance with this homework question pleaseQ2 class=

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EstrellaA412652 EstrellaA412652
  • 03-11-2022

Recall that:

[tex](f\cdot g)(x)=f(x)g(x)\text{.}[/tex]

Then, if:

[tex]\begin{gathered} x\in\text{Dom(f)}\cap Dom(g) \\ \text{then} \\ x\in\text{Dom(f}\cdot g)\text{.} \end{gathered}[/tex]

Now, notice that:

[tex]\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}[/tex]

Therefore:

[tex]\text{Dom(f}\cdot g)=\text{Dom(f)}\cap Dom(g).[/tex]

Answer: True.

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