Relations and Functions
NCERT Class 12
CBSE
Grade 12
Question:
Show that the function $f: \mathbb{N} \rightarrow \mathbb{N}$ given by $f(1) = f(2) = 1$ and $f(x) = x - 1$ for every $x > 2$ is onto but not one-one.
Step-by-Step Solution
Not one-one: $f(1) = f(2) = 1$. [1.0 Mark]
Onto: $1$ is image of $1$, for $y>1$, pre-image is $y+1 \in \mathbb{N}$. Proved! [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Disproving One-one: 1.0 Mark
Proving Onto: 1.0 Mark
Correct Answer:
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