Relations and Functions
NCERT Exemplar Class 12
CBSE
Grade 12
Question:
Let $f: W \to W$ be defined as $f(n) = n - 1$, if $n$ is odd and $f(n) = n + 1$, if $n$ is even. Show that $f$ is invertible. Find the inverse of $f$.
Step-by-Step Solution
Evaluate $(f \circ f)(n) = n$ for both even and odd $n$. [2.0 Marks]
Conclude $f$ is invertible and $f^{-1} = f$. [1.0 Mark]
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🎯 Official CBSE Marking Scheme:
Evaluating composition $(f \circ f)(n) = n$: 2.0 Marks
Concluding $f$ is self-inverse ($f^{-1} = f$): 1.0 Mark
Correct Answer:
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