Let A = {x ∈ R : −4 ≤ x ≤ 4 and x ≠ 0} and f : A → R be defined by

Question:

Let $A=\{x \in R:-4 \leq x \leq 4$ and $x \neq 0\}$ and $f: A \rightarrow R$ be defined by $f(x)=\frac{|x|}{x}$. Write the range of $f$.

Solution:

$\because f(x)=\frac{|x|}{x}=\frac{\pm x}{x}=\pm 1 \forall x \in A$, range of $f=\{-1,1\}$