Question
If $f$ and $g$ are both even functions, is the product $f g$ even? If $f$ and $g$ are both odd functions, is $f g$ odd? What if $f$ is even and $g$ is odd? Justify your answers.
Step 1
- A function $f$ is odd if $f(-x) = -f(x)$ for all $x$ in the domain. Step 2: Let's examine the case where both $f$ and $g$ are even functions. For the product $fg$, we need to check if $(fg)(-x) = (fg)(x)$ for all $x$. $(fg)(-x) = f(-x) \cdot g(-x)$ Since $f$ Show more…
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