Linear functions with absolute values

1003049204

Level: 
C
Let \( f(x)=|x| \). Identify which of the statements is false.
\( \forall a\text{, }b\in\mathbb{R}\colon f(a+b)=f(a)+f(b) \)
\( \forall a\text{, }b\in\mathbb{R}\colon f(a\cdot b)=f(a)\cdot f(b) \)
\( \forall a\in\mathbb{R}\text{, }b\in\mathbb{R}\setminus\{0\}\colon f(\frac ab)=\frac{f(a)}{f(b)} \)
\( \forall a\in\mathbb{R}\colon f(a)=f(-a) \)