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Relations and Functions
NCERT Class 12
CBSE
Grade 12
Question:
Show that the Signum Function $f: \mathbb{R} \rightarrow \mathbb{R}$, given by $f(x) = 1$ if $x > 0$, $0$ if $x = 0$, $-1$ if $x < 0$ is neither one-one nor onto.
Step-by-Step Solution
Not one-one: $f(1) = f(2) = 1$ for distinct $1, 2$. [1.0 Mark] Not onto: Range $= \{-1, 0, 1\} eq \mathbb{R}$. Proved! [1.0 Mark]
--- 🎯 Official CBSE Marking Scheme: Disproving One-one with counterexample: 1.0 Mark Disproving Onto with range analysis: 1.0 Mark
Correct Answer:
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