Functions
Odd/Even Functions
Premium Question
Grade 12
Question:
If $f(x)$ is an odd function and $g(x)$ is an even function, then which of the following is odd?
(1) $f(x) + g(x)$
(2) $f(g(x))$
(3) $g(f(x))$
(4) $f(x) \cdot g(x)$
Step-by-Step Solution
Key Concept: Check each option at $-x$: use $f(-x) = -f(x)$ and $g(-x) = g(x)$. A function $h$ is odd if $h(-x) = -h(x)$ for all $x$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (4)