Question

Graphs of functions are given. Mark option

• A. If f(x) = 3f(−x)
• B. If f(x) = f(−x)
• C. If f(x) = −f(−x)
• D. If 3f(x) = 6f(−x)

Hint:

If the graph has origin symmetry (rotational symmetry $180^\circ$), the function is odd: $f(x) = -f(-x)$.

Answer 1

The Correct Option is C

From the graph: - For $x = 2$, $f(2) = -1$. - For $x = -2$, $f(-2) = 1$. Clearly, $f(2) = - f(-2)$. Similarly for other symmetric points: $f(3) = - f(-3)$. This is the definition of an odd function: \[ f(x) = -f(-x) \quad \forall x \] Thus the correct option is (3). \[ \boxed{f(x) = -f(-x)} \]