The signum function \( f:R\to R \) , defined by
\( \displaystyle f(x)=\begin{cases}-1 & ,x\lt 0\\0 & x=0\\1 & x\gt 0\end{cases} \)
is: (Where R is set of real numbers)
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Neither one-one nor onto
Not one-one: different inputs give the same output, for example
\( \displaystyle f(1)=f(2)=1 \)
Not onto: the range is {−1, 0, 1}, which is not the whole co-domain R. For example, 2 has no pre-image.
So f is neither one-one nor onto.