Functions
Periodicity
Premium Question
Grade 12
Question:
If $f(x + 3) + f(x) = 2$ for all real $x$, then the period of $f$ is:
(1) $3$
(2) $4$
(3) $6$
(4) $12$
Step-by-Step Solution
Key Concept: Replace $x$ by $x + 3$ in the given equation to get a second relation. Combine the two equations to express $f(x + 6)$ in terms of $f(x)$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (3)