Answer
1. $h(x)=f(x)g(x)$
2. $h(-x)=f(-x)g(-x)$
3. $h(-x)=-f(x)g(x)$
4. $h(-x)=-h(x)$
1. Let function $h$ be the product of odd function $f$ and even function $g$.
2. Evaluate for $h(-x)$
3. $f$ is odd so $f(-x)=-f(x)$; $g(x)$ is even so $g(-x)=g(x)$
4. Substitution
Therefore the product of an odd function and an even function is odd.
Work Step by Step
See proof above
